Okay, so I have this chemistry problem here. Let me try to work through it step by step. Let's see what the question is asking. 

The problem says we have a solution with a volume of 200.00 cm³, which is 0.200 L. The solution contains 1.00 g of KH₂PO₄ and 1.00 g of Na₂HPO₄·2H₂O. The temperature is 25°C. We need to find the concentration of orthophosphate ions in this solution. The options are given from A to D.

First, I need to understand what the question is asking. Orthophosphate ions are PO₄³⁻. The two compounds given are KH₂PO₄ (which is potassium dihydrogen phosphate) and Na₂HPO₄·2H₂O (sodium phosphate dihydrate). Let me think about their dissociation in water.

KH₂PO₄ dissociates into K⁺ and H₂PO₄⁻. Similarly, Na₂HPO₄·2H₂O dissociates into 2Na⁺ and HPO₄²⁻, along with the two water molecules. Wait, but the water of crystallization might affect the formula. Let me check. The formula for Na₂HPO₄·2H₂O is correct as given. When it dissolves, it would release Na⁺ ions and HPO₄²⁻ ions. So the solution will have H₂PO₄⁻ and HPO₄²⁻ ions, which are the conjugate base pairs of phosphoric acid. Phosphoric acid has three dissociation steps:

H₃PO₄ ⇌ H⁺ + H₂PO₄⁻ (Ka1 = 7.5×10^-3)
H₂PO₄⁻ ⇌ H⁺ + HPO₄²⁻ (Ka2 = 6.2×10^-8)
HPO₄²⁻ ⇌ H⁺ + PO₄³⁻ (Ka3 = 1.8×10^-12)

Since we have both H₂PO₄⁻ and HPO₄²⁻ in solution, this forms a buffer system. The question is about the concentration of orthophosphate ions, which is PO₄³⁻. That comes from the third dissociation step, which is the deprotonation of HPO₄²⁻. 

So, to find [PO₄³⁻], we can use the Henderson-Hasselbalch equation for the third dissociation. The Henderson-Hasselbalch equation is:

pH = pKa + log([A⁻]/[HA])

But wait, in this case, we need to relate the concentrations of HPO₄²⁻ and PO₄³⁻. So the relevant equation would be:

pH = pKa3 + log([PO₄³⁻]/[HPO₄²⁻])

But we need to find [PO₄³⁻], so rearranging:

[PO₄³⁻] = [HPO₄²⁻] × 10^(pH - pKa3)

But wait, we don't know the pH of the solution. Hmm. Alternatively, since the solution is a buffer between H₂PO₄⁻ and HPO₄²⁻, the pH is determined by their concentrations. Let me think. The buffer consists of HPO₄²⁻ (which is the conjugate base) and H₂PO₄⁻ (the acid). Wait, no. Wait, let's clarify. The first dissociation is H3PO4 → H+ + H2PO4⁻. The second is H2PO4⁻ → H+ + HPO4²⁻. The third is HPO4²⁻ → H+ + PO4³⁻. So, HPO4²⁻ can act as an acid (losing H+ to become PO4³⁻) and H2PO4⁻ can act as a base (gaining H+ to become H3PO4). But in the solution, we have both H2PO4⁻ and HPO4²⁻. So the buffer system is between H2PO4⁻ (acid) and HPO4²⁻ (conjugate base) for the second dissociation. The pH of the solution can be calculated using the Henderson-Hasselbalch equation for the second dissociation:

pH = pKa2 + log([HPO4²⁻]/[H2PO4⁻])

But wait, the problem is that the solution contains both KH2PO4 and Na2HPO4·2H2O. Let me calculate the moles of each to find their concentrations.

First, calculate moles of KH2PO4. The molar mass (Mw) is 136.09 g/mol. Moles = mass / molar mass = 1.00 g / 136.09 g/mol ≈ 0.00735 moles. Since KH2PO4 dissociates into K+ and H2PO4⁻, the concentration of H2PO4⁻ is 0.00735 moles in 0.200 L. So [H2PO4⁻] = 0.00735 / 0.200 ≈ 0.03675 M.

Next, moles of Na2HPO4·2H2O. The molar mass is 177.99 g/mol. Moles = 1.00 g / 177.99 g/mol ≈ 0.00562 moles. Since Na2HPO4·2H2O dissociates into 2Na+ and HPO4²⁻·2H2O, but the water is just part of the formula. However, when dissolved in water, it dissociates completely into HPO4²⁻ and the sodium ions. So the concentration of HPO4²⁻ is 0.00562 moles in 0.200 L. Therefore, [HPO4²⁻] = 0.00562 / 0.200 ≈ 0.0281 M.

Now, the buffer solution consists of H2PO4⁻ (acid) and HPO4²⁻ (base). So the Henderson-Hasselbalch equation for this buffer is:

pH = pKa2 + log([HPO4²⁻]/[H2PO4⁻])

pKa2 is given as 6.2×10^-8. Wait, wait. Wait, no. The problem states that the Ka values are Ka1=7.5e-3, Ka2=6.2e-8, Ka3=1.8e-12. So pKa2 is -log(6.2e-8) ≈ 7.21 (since log(6.2) ≈ 0.79, so 8 - 0.79 ≈ 7.21). Similarly, pKa3 is -log(1.8e-12) ≈ 11.74 (since log(1.8) ≈ 0.255, so 12 - 0.255 ≈ 11.745).

So, applying the Henderson-Hasselbalch equation:

pH = 7.21 + log(0.0281 / 0.03675)
Let me compute the ratio 0.0281 / 0.03675 ≈ 0.765. The log of 0.765 is approximately... log(0.765) ≈ -0.116. So pH ≈ 7.21 - 0.116 ≈ 7.094.

But wait, the pH of the solution is 7.094. Now, since we need to find [PO4³⁻], which comes from the third dissociation of HPO4²⁻. The third dissociation is HPO4²⁻ ⇌ H+ + PO4³⁻. The expression for Ka3 is [H+][PO4³⁻]/[HPO4²⁻] = 1.8e-12. We can rearrange this to solve for [PO4³⁻]:

[PO4³⁻] = (Ka3 * [HPO4²⁻]) / [H+]

But we need to find [H+]. Since we know the pH, [H+] = 10^-pH. pH is approximately 7.094, so [H+] ≈ 10^-7.094 ≈ 8.36e-8 M.

Now, plugging into the equation:

[PO4³⁻] = (1.8e-12 * 0.0281) / (8.36e-8)

Let me compute the numerator first: 1.8e-12 * 0.0281 ≈ 5.058e-14

Denominator: 8.36e-8

So [PO4³⁻] ≈ 5.058e-14 / 8.36e-8 ≈ 6.05e-7 M.

Wait, looking at the options: A is 6.24e-7, B is 3.97e-7, C is 5.48e-7, D is 2.81e-7. So my calculation gives approximately 6.05e-7 M, which is close to option A (6.24e-7). But wait, maybe I made an approximation error. Let me check the steps again.

First, check the moles:

KH2PO4: 1.00 g / 136.09 g/mol. Let me calculate this more accurately. 1 / 136.09 ≈ 0.007352 mol. So 0.007352 mol. Divided by 0.2 L gives 0.03676 M. Correct.

Na2HPO4·2H2O: 1.00 g / 177.99 g/mol. 1 / 177.99 ≈ 0.005621 mol. Divided by 0.2 L gives 0.028105 M. Correct.

Henderson-Hasselbalch equation: pH = pKa2 + log([base]/[acid]) = 7.21 + log(0.028105 / 0.03676) = 7.21 + log(0.765) ≈ 7.21 - 0.116 ≈ 7.094. Correct.

[H+] = 10^-7.094. Let me compute this more accurately. 10^7.094 = 10^7 * 10^0.094. 10^0.094 ≈ 1.245 (since log10(1.245) ≈ 0.094). So 10^7.094 ≈ 1.245e7, so [H+] = 1 / 1.245e7 ≈ 8.03e-8 M. Wait, that's different from my previous calculation. Wait, 10^-7.094 = 1 / 10^7.094. Let me compute 10^7.094:

10^7 = 10,000,000

10^0.094 ≈ 1.245 (as above). So 10^7.094 ≈ 1.245e7. Therefore, 1 / 1.245e7 ≈ 8.03e-8. So [H+] ≈ 8.03e-8 M.

Now, [PO4³⁻] = (1.8e-12 * 0.028105) / 8.03e-8 = (5.0589e-14) / 8.03e-8 ≈ 6.298e-7 M. Hmm, that's approximately 6.3e-7, which is close to option A (6.24e-7). But why is there a discrepancy?

Wait, maybe the approximation for [H+] is too rough. Let me compute 10^-7.094 more accurately. Let's use logarithm tables or a calculator. Alternatively, use the exact value.

Alternatively, maybe I should use the exact pH value from the Henderson-Hasselbalch equation. Let's compute the ratio more precisely.

The ratio [HPO4²⁻]/[H2PO4⁻] is 0.028105 / 0.03676 ≈ 0.765. Let's compute log(0.765) precisely. Using a calculator, log10(0.765) ≈ -0.116. So pH = 7.21 - 0.116 = 7.094. So [H+] = 10^-7.094. Let's compute 10^-7.094 exactly.

Alternatively, use the formula: 10^-7.094 = 10^-7 * 10^-0.094. 10^-7 is 1e-7. 10^-0.094 = 1 / 10^0.094. Let's compute 10^0.094. Let me use natural logarithm for more precision. Let x = 0.094. ln(10^x) = x * ln(10). So ln(10^0.094) ≈ 0.094 * 2.302585 ≈ 0.2155. Then, 10^0.094 = e^0.2155 ≈ 1.24 (since e^0.2155 ≈ 1 + 0.2155 + 0.0232 + 0.0013 ≈ 1.239). So 10^0.094 ≈ 1.24. Therefore, 10^-0.094 ≈ 1/1.24 ≈ 0.806. Therefore, 10^-7.094 ≈ 1e-7 * 0.806 ≈ 8.06e-8. So [H+] ≈ 8.06e-8 M.

Now, [PO4³⁻] = (1.8e-12 * 0.028105) / 8.06e-8 = (5.0589e-14) / 8.06e-8 ≈ 6.27e-7 M. That's approximately 6.27e-7, which is very close to option A (6.24e-7). However, the options don't have exactly 6.27e-7. The closest is A (6.24e-7). But maybe there's a more precise calculation.

Alternatively, maybe I made a mistake in the initial assumption. Let me check the dissociation steps again. The problem is about the concentration of orthophosphate ions, which is PO4³⁻. The source of PO4³⁻ is the third dissociation of HPO4²⁻. So the reaction is HPO4²⁻ ⇌ H+ + PO4³⁻. The equilibrium expression is Ka3 = [H+][PO4³⁻]/[HPO4²⁻]. Therefore, [PO4³⁻] = (Ka3 * [HPO4²⁻]) / [H+]. That's correct.

But perhaps the [H+] isn't exactly 10^-pH? Wait, in the solution, the pH is determined by the buffer system between H2PO4⁻ and HPO4²⁻. The pH we calculated is correct for that buffer. So [H+] is indeed 10^-7.094 ≈ 8.06e-8 M.

So plugging in:

[PO4³⁻] = (1.8e-12 * 0.028105) / 8.06e-8 ≈ (5.0589e-14) / 8.06e-8 ≈ 6.27e-7 M.

But the options are A: 6.24e-7, B: 3.97e-7, C:5.48e-7, D:2.81e-7. So 6.27e-7 is closest to A. But why is there a discrepancy between my calculation and the option? Maybe I need to check the initial moles again.

Wait, let me recalculate the moles of KH2PO4 and Na2HPO4·2H2O.

KH2PO4: 1.00 g / 136.09 g/mol.

136.09 g/mol is the molar mass. So 1.00 / 136.09 = approximately 0.007352 mol. Then divided by 0.200 L gives 0.03676 M. Correct.

Na2HPO4·2H2O: 1.00 g / 177.99 g/mol. 1 / 177.99 ≈ 0.005620 mol. Divided by 0.200 L gives 0.02810 M. Correct.

So the concentrations are correct. Then the ratio is 0.02810 / 0.03676 = 0.765. Log(0.765) is -0.116. pH = 7.21 - 0.116 = 7.094. Correct.

Then [H+] = 10^-7.094 ≈ 8.06e-8. Then [PO4³⁻] = (1.8e-12 * 0.02810) / 8.06e-8. Let's compute 1.8e-12 * 0.02810 = 5.058e-14. Divided by 8.06e-8: 5.058e-14 / 8.06e-8 ≈ 6.27e-7. So yes, 6.27e-7. 

But the options don't have 6.27e-7. The closest is A (6.24e-7). Maybe the values in the problem are rounded. Let's check if the problem uses exact values for the molar masses.

Wait, the problem gives Mw of KH2PO4 as 136.09 g/mol. Let me confirm the actual molar mass of KH2PO4. The formula is K(H2PO4). K is 39.10 g/mol. H2PO4 is (2*1.008) + 30.97 (P) + 4*16.00 (O) = 2 + 30.97 + 64 = 96.97. So total molar mass is 39.10 + 96.97 = 136.07 g/mol. The problem states 136.09, which is very close. So that's correct.

Similarly, Na2HPO4·2H2O. The formula is Na2HPO4·2H2O. Molar mass: 2*(22.99) (Na) + (30.97) (P) + 4*16 (O) + 2*(18) (H2O) = 2*22.99 = 45.98; 30.97; 4*16=64; 2*18=36. Total: 45.98 + 30.97 + 64 + 36 = 176.95 g/mol. The problem states 177.99, which is a bit higher. Wait, maybe I made a mistake. Let me calculate again.

Wait, Na2HPO4·2H2O: the formula is Na2HPO4·2H2O. So:

Na: 2 atoms × 22.99 = 45.98 g/mol

H: in HPO4: 1 H; in 2H2O: 4 H. Total H: 1 + 4*2 = 9 H. Wait, wait, no. Each H2O has 2 H. So 2 H2O contribute 4 H. The HPO4 has 1 H. So total H: 1 + 4 = 5 H. But wait, the molecular formula is HPO4·2H2O. So HPO4 has 1 H, and 2 H2O each have 2 H, so total H is 1 + 4 = 5. So total H: 5.

But the molar mass calculation is:

Na: 2 × 22.99 = 45.98

H: 5 × 1.008 = 5.04

P: 30.97

O: 4 (from HPO4) + 2×2 (from H2O) = 8 O. So 8 × 16 = 128.

Total molar mass: 45.98 + 5.04 + 30.97 + 128 = 45.98 + 5.04 = 51.02; 51.02 + 30.97 = 81.99; 81.99 + 128 = 209.99 g/mol. Wait, that can't be right. Wait, maybe I messed up the formula.

Wait, the formula is Na2HPO4·2H2O. So the formula unit is Na2HPO4 plus 2 H2O. So:

Na: 2 atoms × 22.99 = 45.98

H: in HPO4: 1 H; in 2H2O: 4 H → total 5 H.

P: 1 × 30.97 = 30.97

O: HPO4 has 4 O, 2H2O has 2×1 O each → 4 + 2×1 = 6 O.

Wait, that's not right. H2O has O. Each H2O has one O. So 2 H2O contribute 2 O. So total O: 4 (from HPO4) + 2 (from H2O) = 6 O. So O: 6 × 16 = 96.

H: 5 × 1.008 = 5.04

So total molar mass: 45.98 (Na) + 5.04 (H) + 30.97 (P) + 96 (O) = 45.98 + 5.04 = 51.02; 51.02 + 30.97 = 81.99; 81.99 + 96 = 177.99 g/mol. Ah, so that's correct. So the problem's molar mass is accurate. So my previous calculation was correct.

Therefore, the moles are correct. Then the rest of the steps are correct. So the result is approximately 6.27e-7 M. But the closest option is A (6.24e-7). Hmm. But maybe the problem expects a different approach. Let me think again.

Wait, maybe the problem is considering the third dissociation as the source of PO4³⁻, but perhaps there's another factor. Wait, in the solution, the PO4³⁻ comes from HPO4²⁻ losing a proton. But in the solution, HPO4²⁻ is present, and it's in equilibrium with PO4³⁻. However, the solution also contains H2PO4⁻, which can act as an acid (donate H+) and HPO4²⁻ as its conjugate base. So the solution is a buffer between H2PO4⁻ and HPO4²⁻, and the pH is determined by that buffer.

But the PO4³⁻ concentration comes from the third dissociation of HPO4²⁻. The problem is, perhaps the assumption that the pH is determined only by the buffer between H2PO4⁻ and HPO4²⁻ is correct, but maybe there's a contribution from another source? Or perhaps the solution is not just a buffer but also considering other factors?

Alternatively, perhaps the problem expects the use of the Henderson-Hasselbalch equation for the third dissociation. Let me try that.

The third dissociation is HPO4²⁻ ⇌ H+ + PO4³⁻, with Ka3 = 1.8e-12. The Henderson-Hasselbalch equation here is:

pH = pKa3 + log([PO4³⁻]/[HPO4²⁻])

Wait, but actually, in this case, the base is HPO4²⁻ and the acid is PO4³⁻. Wait no, the equation is:

For the reaction: HPO4²⁻ ⇌ H+ + PO4³⁻

The Henderson-Hasselbalch equation is:

pH = pKa3 + log([PO4³⁻]/[HPO4²⁻])

But wait, the Henderson-Hasselbalch equation is pH = pKa + log([base]/[acid]). Here, the base is PO4³⁻ (since it's the conjugate base of HPO4²⁻), and the acid is HPO4²⁻ (since it can donate a proton to become PO4³⁻). So the equation is:

pH = pKa3 + log([PO4³⁻]/[HPO4²⁻])

But we already calculated the pH using the buffer between H2PO4⁻ and HPO4²⁻. So the pH we found (7.094) is the pH of the solution, which is also the pH relevant for the third dissociation. Therefore, we can use the Henderson-Hasselbalch equation for the third dissociation to find [PO4³⁻].

So let's set up the equation:

7.094 = -log(1.8e-12) + log([PO4³⁻]/[HPO4²⁻])

pKa3 is -log(1.8e-12) ≈ 11.74 (since log(1.8) ≈ 0.255, so 12 - 0.255 = 11.745). Therefore:

7.094 = 11.745 + log([PO4³⁻]/[HPO4²⁻])

Rearranging:

log([PO4³⁻]/[HPO4²⁻]) = 7.094 - 11.745 = -4.651

Therefore:

[PO4³⁻]/[HPO4²⁻] = 10^-4.651 ≈ 2.24e-5

Therefore, [PO4³⁻] = [HPO4²⁻] × 2.24e-5

Wait, but [HPO4²⁻] is 0.02810 M, so:

[PO4³⁻] = 0.02810 × 2.24e-5 ≈ 6.29e-7 M. Which is the same as before. So this gives the same result. So this approach also leads to approximately 6.29e-7 M. So the answer should be around 6.29e-7, but the closest option is A (6.24e-7). Hmm.

Wait, but let me check the calculation again. Let's compute 0.02810 * 2.24e-5:

0.02810 × 2.24e-5 = 0.02810 * 0.0000224 = 0.02810 * 2.24e-5 = 6.29e-7. Yes, that's correct. So again, 6.29e-7. Still, the closest option is A (6.24e-7). But why the discrepancy?

Alternatively, maybe there's a miscalculation in the pH. Let me recheck the pH calculation.

We have the buffer between H2PO4⁻ and HPO4²⁻. The concentrations are [H2PO4⁻] = 0.03676 M and [HPO4²⁻] = 0.02810 M. The Henderson-Hasselbalch equation is:

pH = pKa2 + log([HPO4²⁻]/[H2PO4⁻])

pKa2 is 7.21 (since Ka2 = 6.2e-8 → pKa2 = -log(6.2e-8) ≈ 7.21). So:

pH = 7.21 + log(0.02810 / 0.03676) = 7.21 + log(0.765) ≈ 7.21 - 0.116 = 7.094. Correct.

Alternatively, maybe the problem expects the use of the exact expression for the third dissociation without assuming the pH from the first two steps. Let me think. Wait, but the solution's pH is determined by the first two buffer systems, so the third dissociation's contribution is negligible. So the approach is correct.

Alternatively, perhaps the problem is asking for the concentration of the conjugate base of the third dissociation, but in this case, the PO4³⁻ is the conjugate base. Wait, no, the PO4³⁻ is the conjugate base of HPO4²⁻. So the approach is correct.

Wait, maybe there's a mistake in the calculation of [PO4³⁻] = [HPO4²⁻] × 10^(pKa3 - pH). Wait, no. Let me re-express the Henderson-Hasselbalch equation correctly.

The Henderson-Hasselbalch equation is:

pH = pKa + log([base]/[acid])

In this case, base is PO4³⁻, acid is HPO4²⁻. So:

pH = pKa3 + log([PO4³⁻]/[HPO4²⁻])

Which rearranges to:

[PO4³⁻]/[HPO4²⁻] = 10^(pH - pKa3)

So [PO4³⁻] = [HPO4²⁻] × 10^(pH - pKa3)

pH is 7.094, pKa3 is 11.745. So:

[PO4³⁻] = 0.02810 × 10^(7.094 - 11.745) = 0.02810 × 10^(-4.651) ≈ 0.02810 × 2.24e-5 ≈ 6.29e-7 M. Correct.

But none of the options exactly match this. Option A is 6.24e-7, which is very close. Maybe the problem expects rounding to two significant figures. Let's check the given Ka values. The Ka values are given to three significant figures (7.5x10^-3, 6.2x10^-8, 1.8x10^-12). The volumes are given to three significant figures (200.00 cm³ is four significant figures). The masses are given to three significant figures (1.00 g is three). So the answer should be given to three significant figures. 6.29e-7 rounds to 6.29e-7. But the options are:

A. 6.24e-7

B. 3.97e-7

C. 5.48e-7

D. 2.81e-7

So 6.29e-7 is 6.3e-7 when rounded to two significant figures. But the options have A as 6.24e-7, which is 6.24 x10^-7. So perhaps the exact calculation would give 6.24e-7. Let me check with more precise numbers.

Let me recalculate the pH and the subsequent steps with more precision.

First, calculate the ratio [HPO4²⁻]/[H2PO4⁻] = 0.028105 / 0.03676 = 0.76503.

log(0.76503) = log(76503e-5) = log(7.6503e-1) = log(7.6503) + log(10^-1) = 0.8839 - 1 = -0.1161. So pH = 7.21 + (-0.1161) = 7.0939. So pH = 7.0939.

Then, [PO4³⁻] = [HPO4²⁻] × 10^(pH - pKa3) = 0.028105 × 10^(7.0939 - 11.745). Let's compute the exponent:

7.0939 - 11.745 = -4.6511. So 10^-4.6511 = 10^(-4 - 0.6511) = 10^-4 × 10^-0.6511.

10^-4 = 0.0001.

10^-0.6511 ≈ 0.223 (since 10^-0.65 = approx 0.2236). Let me compute 10^-0.6511:

Using logarithm tables or a calculator:

Let me compute ln(10^-0.6511) = -0.6511 * ln(10) ≈ -0.6511 * 2.302585 ≈ -1.499. So exp(-1.499) ≈ 0.223. Therefore, 10^-0.6511 ≈ 0.223.

Therefore, 10^-4.6511 ≈ 0.0001 * 0.223 = 0.0000223.

Then, [PO4³⁻] = 0.028105 * 0.0000223 ≈ 0.028105 * 0.0000223.

Let me compute this multiplication:

0.028105 * 0.0000223 = 0.028105 * 2.23e-5 = (0.028105 * 2.23) e-5.

0.028105 * 2.23 ≈ 0.06264. So 0.06264e-5 = 6.264e-7 M. So approximately 6.26e-7.

Looking at the options, A is 6.24e-7, which is very close. Maybe the exact calculation with more precise numbers would give 6.24e-7. Let me check with more precise values.

Alternatively, perhaps the problem uses the exact Ka values without approximating pKa. Let me recalculate using exact pKa values.

Ka2 = 6.2x10^-8 → pKa2 = log(1/(6.2e-8)) = log(1) - log(6.2e-8) = 0 - (log(6.2) + log(1e-8)) = - (0.7924 + (-8)) = 7.2076. So pKa2 ≈ 7.2076.

Ka3 = 1.8x10^-12 → pKa3 = log(1/(1.8e-12)) = log(1) - log(1.8e-12) = 0 - (log(1.8) + log(1e-12)) = - (0.2553 + (-12)) = 11.7447.

So pH = pKa2 + log([HPO4²⁻]/[H2PO4⁻]) = 7.2076 + log(0.028105 / 0.03676) = 7.2076 + log(0.76503) = 7.2076 + (-0.1161) = 7.0915.

So pH = 7.0915.

Then, [PO4³⁻] = [HPO4²⁻] × 10^(pH - pKa3) = 0.028105 × 10^(7.0915 - 11.7447) = 0.028105 × 10^(-4.6532).

Compute 10^(-4.6532) = 10^(-4 -0.6532) = 10^-4 × 10^-0.6532.

10^-0.6532 ≈ 0.222 (using calculator: 10^0.6532 = 4.495 → 1/4.495 ≈ 0.2226). So 10^-0.6532 ≈ 0.2226.

Therefore, 10^-4.6532 ≈ 0.0001 × 0.2226 = 0.00002226.

Then, [PO4³⁻] = 0.028105 × 0.00002226 ≈ 0.028105 × 0.00002226 ≈ 0.000000625 → 6.25e-7 M.

Still, the result is approximately 6.25e-7, which is closest to option A (6.24e-7). The slight discrepancy might be due to rounding during intermediate steps. Alternatively, perhaps the problem expects the answer to be 6.24e-7, which is option A.

Alternatively, maybe there's a mistake in the approach. Let me think again. Another approach: perhaps the PO4³⁻ comes from HPO4²⁻ dissociating, but since the solution is a buffer between H2PO4⁻ and HPO4²⁻, the concentration of PO4³⁻ is negligible compared to HPO4²⁻. Wait, but the problem is asking for the orthophosphate ions, which are PO4³⁻. So the only source is the third dissociation. Therefore, the approach is correct.

Alternatively, maybe the problem considers the total phosphate species, but no, the question is specifically about orthophosphate ions (PO4³⁻). So the approach is correct.

Alternatively, perhaps the problem is using the formula for the concentration of the conjugate base in the third dissociation. Let me check.

The third dissociation is HPO4²⁻ ⇌ H+ + PO4³⁻. The equilibrium expression is Ka3 = [H+][PO4³⁻]/[HPO4²⁻]. Rearranged, [PO4³⁻] = (Ka3 [HPO4²⁻]) / [H+].

Which is the same as before. So the calculation is correct.

Alternatively, maybe the question is asking for the total phosphate concentration, but no, it's specifically orthophosphate ions. So the approach is correct.

Therefore, the answer should be approximately 6.24e-7 M, which is option A. But why the slight discrepancy? Let me check the exact calculation with more precise numbers.

Let me compute [PO4³⁻] = (1.8e-12 * 0.028105) / 8.06e-8.

1.8e-12 * 0.028105 = 5.0589e-14.

8.06e-8 = 8.06e-8.

5.0589e-14 / 8.06e-8 = (5.0589 / 8.06) * 1e-6 = 0.627 * 1e-6 = 6.27e-7. So 6.27e-7. Still, the closest option is A (6.24e-7). Maybe the problem uses a different value for the molar mass of KH2PO4 or Na2HPO4·2H2O. Let me check again.

Molar mass of KH2PO4: 136.09 g/mol. The problem gives 136.09, which is correct. Na2HPO4·2H2O: 177.99 g/mol, which matches the problem's data. So the moles are correct.

Alternatively, perhaps the problem uses a different value for the third dissociation's pKa. Let me check the given Ka values. Yes, Ka3 is 1.8e-12. So pKa3 is 11.745. Correct.

Alternatively, maybe the problem uses the formula [PO4³⁻] = Ka3 * ([HPO4²⁻]/[H+]). Let me compute [H+] again. pH is 7.094, so [H+] = 10^-7.094 ≈ 8.06e-8 M. Correct.

Alternatively, maybe the problem uses a different value for the second dissociation's pKa. Let me check the given Ka2: 6.2e-8. So pKa2 is log(1/6.2e-8) = log(1) - log(6.2e-8) = 0 - (log(6.2) + log(1e-8)) = -(0.7924 + (-8)) = 7.2076. Correct.

Hmm. Given all that, the calculation seems correct, leading to approximately 6.27e-7 M. The closest option is A (6.24e-7). Perhaps the problem expects rounding to three significant figures, which would make 6.27e-7 ≈ 6.27e-7, which is not an option. Alternatively, maybe there's a mistake in the problem's given values. For example, if the molar mass of Na2HPO4·2H2O was different, but the problem states 177.99 g/mol, which is correct.

Alternatively, maybe the problem uses the Henderson-Hasselbalch equation in a different way. Let me check again. The Henderson-Hasselbalch equation for the third dissociation is:

pH = pKa3 + log([PO4³⁻]/[HPO4²⁻])

So [PO4³⁻] = [HPO4²⁻] * 10^(pH - pKa3)

pH - pKa3 = 7.094 - 11.745 = -4.651

10^-4.651 ≈ 2.23e-5

So [PO4³⁻] = 0.02810 * 2.23e-5 ≈ 6.27e-7. Correct.

Therefore, the answer should be approximately 6.27e-7, but since the options don't have that, the closest is A (6.24e-7). Alternatively, maybe there's a miscalculation in the problem's given data. But based on the given information, the correct answer should be approximately 6.24e-7, which is option A.
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