Question

How many grams of sulfuric acid are needed to produce 57.0 grams of water? Show all steps of your calculation as well as the final answer.
2NaOH+H2SO4 > 2Na2SO4+2H2O

Answer 1

Answer:

155.16 g.

Explanation:

• Firstly, It is considered as a stichiometry problem.

• From the balanced equation: 2NaOH + H₂SO₄ → 2Na₂SO₄ + 2H₂O

• It is clear that the stichiometry shows that 2.0 moles of NaOH reacts with 1.0 mole of H₂SO₄ to give 2.0 moles of Na₂SO₄ and 2.0 moles of H₂O.

• We must convert the grams of water (57.0 g) to moles (n = mass/molar mass).

• n = (57.0 g) / (18.0 g/mole) = 3.1666 moles.

• Now, we can get the number of moles of H₂SO₄ that is needed to produce 3.1666 moles of water.

• Using cross multiplication:

• 1.0 mole of H₂SO₄ → 2.0 moles of H₂O, from the stichiometry of the balanced equation.

• ??? moles of H₂SO₄ → 3.1666 moles of H₂O.

• The number of moles of H₂SO₄ that will produce 3.1666 moles of H₂O (57.0 g) is (1.0 x 3.1666 / 2.0) = 1.5833 moles.

• Finally, we should convert the number of moles of H₂SO₄ into grams (n = mass/molar mass).

• Molar mass of H₂SO₄ = 98.0 g/mole.

• mass = n x molar mass = (1.5833 x 98.0) = 155.16 g.

Answer 2

Answer: 155.134 grams of sulfuric acid is needed.

Explanation:

To calculate the moles, we use the following equation:

$\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}$

Moles of water:

Given mass of water = 57 grams

Molar mass of water = 18 g/mol

Putting values in above equation, we get:

$\text{Number of moles}=\frac{57g}{18g/mol}=3.166moles$

For the given chemical reaction, the equation follows:

$2NaOH+H_2SO_4\rightarrow 2Na_2SO_4+2H_2O$

By Stoichiometry of the reaction:

2 moles of water are produced by 1 mole of sulfuric acid

So, 3.166 moles of water will produced by = $\frac{1}{2}\times 3.166=1.583moles$ of sulfuric acid.

Now, to calculate the mass of sulfuric acid, we use the moles equation:

Molar mass of sulfuric acid = 98 g/mol

Putting values in above equation, we get:

$1.583mol=\frac{\text{Given mass}}{98g/mol}$

Mass of sulfuric acid = 155.134 grams

Hence, 155.134 grams of sulfuric acid is needed.