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Math  /  Algebra

Question3KOH+H3PO4→ K3PO4+3H2O3 \mathrm{KOH}+\mathrm{H}_{3} \mathrm{PO}_{4} \rightarrow \mathrm{~K}_{3} \mathrm{PO}_{4}+3 \mathrm{H}_{2} \mathrm{O} how many grams of potassium phosphate, K3PO4\mathrm{K}_{3} \mathrm{PO}_{4}, are produced from 30.3 g of potassium hydroxide, KOH ? mass of potassium phosphate: □\square

Studdy Solution

STEP 1

1. The chemical reaction is balanced as given: 3KOH+H3PO4→K3PO4+3H2O3 \mathrm{KOH} + \mathrm{H}_{3} \mathrm{PO}_{4} \rightarrow \mathrm{K}_{3} \mathrm{PO}_{4} + 3 \mathrm{H}_{2} \mathrm{O}.
2. We are given 30.3 g of potassium hydroxide (KOH).
3. We need to find the mass of potassium phosphate (K3PO4\mathrm{K}_{3} \mathrm{PO}_{4}) produced.
4. Molar masses: - KOH = 39.10 (K) + 16.00 (O) + 1.01 (H) = 56.11 g/mol - K3PO4\mathrm{K}_{3} \mathrm{PO}_{4} = 3(39.10) (K) + 30.97 (P) + 4(16.00) (O) = 212.27 g/mol

STEP 2

1. Calculate the moles of KOH.
2. Use stoichiometry to find the moles of K3PO4\mathrm{K}_{3} \mathrm{PO}_{4}.
3. Calculate the mass of K3PO4\mathrm{K}_{3} \mathrm{PO}_{4}.

STEP 3

Calculate the moles of KOH.
Using the formula: Moles of KOH=Mass of KOHMolar mass of KOH\text{Moles of KOH} = \frac{\text{Mass of KOH}}{\text{Molar mass of KOH}}
Moles of KOH=30.3 g56.11 g/mol≈0.540 moles\text{Moles of KOH} = \frac{30.3 \text{ g}}{56.11 \text{ g/mol}} \approx 0.540 \text{ moles}

STEP 4

Use stoichiometry to find the moles of K3PO4\mathrm{K}_{3} \mathrm{PO}_{4}.
From the balanced equation, 3 moles of KOH produce 1 mole of K3PO4\mathrm{K}_{3} \mathrm{PO}_{4}.
Moles of K3PO4=0.540 moles KOH3≈0.180 moles\text{Moles of } \mathrm{K}_{3} \mathrm{PO}_{4} = \frac{0.540 \text{ moles KOH}}{3} \approx 0.180 \text{ moles}

STEP 5

Calculate the mass of K3PO4\mathrm{K}_{3} \mathrm{PO}_{4}.
Using the formula: Mass of K3PO4=Moles of K3PO4×Molar mass of K3PO4\text{Mass of } \mathrm{K}_{3} \mathrm{PO}_{4} = \text{Moles of } \mathrm{K}_{3} \mathrm{PO}_{4} \times \text{Molar mass of } \mathrm{K}_{3} \mathrm{PO}_{4}
Mass of K3PO4=0.180 moles×212.27 g/mol≈38.21 g\text{Mass of } \mathrm{K}_{3} \mathrm{PO}_{4} = 0.180 \text{ moles} \times 212.27 \text{ g/mol} \approx 38.21 \text{ g}
The mass of potassium phosphate produced is:
38.21 g\boxed{38.21 \text{ g}}

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