Question

How many grams of sodium sulfate Na2SO4 can be made if you start with a limited amount of 50.0 grams of sodium hydroxide NaOH and more than enough sulfuric acid?
2 NaOH + H2SO4  Na2SO4 + 2 H2O
Responses

88.75 g
88.75 g

6.67 g
6.67 g

6.75 g
6.75 g

322 g

Answer 1

To determine how many grams of sodium sulfate (Na2SO4) can be produced from 50.0 grams of sodium hydroxide (NaOH) and excess sulfuric acid (H2SO4), we first need to find out how many moles of NaOH are present and then use the stoichiometry of the reaction.

### Step 1: Calculate moles of NaOH

The molar mass of NaOH is:
- Na: 22.99 g/mol
- O: 16.00 g/mol
- H: 1.01 g/mol

So, the molar mass of NaOH = 22.99 + 16.00 + 1.01 = **40.00 g/mol**.

Now, we can find the number of moles of NaOH in 50.0 grams:
\[
\text{Moles of NaOH} = \frac{\text{Mass}}{\text{Molar Mass}} = \frac{50.0 \text{ g}}{40.00 \text{ g/mol}} = 1.25 \text{ moles NaOH}
\]

### Step 2: Use stoichiometry of the reaction

The balanced chemical equation is:
\[
2 \text{NaOH} + \text{H}_2\text{SO}_4 \rightarrow \text{Na}_2\text{SO}_4 + 2 \text{H}_2\text{O}
\]

From the equation, we see that 2 moles of NaOH produce 1 mole of Na2SO4. Therefore, 1.25 moles of NaOH will produce:
\[
\text{Moles of Na2SO4} = \frac{1.25 \text{ moles NaOH}}{2} = 0.625 \text{ moles Na2SO4}
\]

### Step 3: Calculate grams of Na2SO4

Now we will convert moles of Na2SO4 to grams. The molar mass of Na2SO4 is:
- Na: 22.99 g/mol x 2 = 45.98 g/mol
- S: 32.07 g/mol
- O: 16.00 g/mol x 4 = 64.00 g/mol

So, the molar mass of Na2SO4 = 45.98 + 32.07 + 64.00 = **142.05 g/mol**.

Now, we can find the mass of Na2SO4 produced:
\[
\text{Mass of Na2SO4} = \text{Moles} \times \text{Molar Mass} = 0.625 \text{ moles} \times 142.05 \text{ g/mol} \approx 88.78 \text{ g}
\]

### Conclusion

The closest answer from the options provided is **88.75 g** (which likely rounds from the calculated value of 88.78 g).

So, the answer is **88.75 g**.