Question

When small quantities of elemental hydrogen gas are needed for laboratory work, the hydrogen is often generated by chemical reaction of a metal with acid. For example, zinc reacts with hydrochloric acid, releasing gaseous elemental hydrogen: $$ \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ What mass of hydrogen gas is produced when \(2.50 \mathrm{~g}\) of zine is reacted with excess aqueous hydrochloric acid?

Short answer

When \(2.50 \ \text{g}\) of zinc reacts with excess aqueous hydrochloric acid, \(0.0771 \ \text{g}\) of hydrogen gas is produced.

Step-by-step solution

Determine the molar mass of the substances involved#important# In order to perform stoichiometric calculations, we need to know the molar mass of zinc and hydrogen: - Molar mass of zinc (Zn): 65.38 g/mol - Molar mass of hydrogen (H₂): 2.02 g/mol

Step 2: Calculate moles of zinc reacted#important# To find the moles of zinc reacted, we can use the given mass (2.50 g) and the molar mass of zinc (65.38 g/mol): $$ \text{moles of Zn} = \frac{\text{mass of Zn}}{\text{molar mass of Zn}} = \frac{2.50 \ \text{g}}{65.38 \ \text{g/mol}} = 0.0382 \ \text{mol} $$

Calculate moles of hydrogen produced#important# The stoichiometric ratio between Zn and H₂ from the balanced equation is 1:1. Therefore, the moles of hydrogen produced would be the same as the moles of zinc reacted: $$ \text{moles of H₂} = \text{moles of Zn} = 0.0382 \ \text{mol} $$

Step 4: Calculate mass of hydrogen produced#important# Finally, we can calculate the mass of hydrogen gas produced by using the calculated moles of hydrogen and its molar mass (2.02 g/mol): $$ \text{mass of H₂} = \text{moles of H₂} \times \text{molar mass of H₂} = 0.0382 \ \text{mol} \times 2.02 \ \text{g/mol} = 0.0771 \ \text{g} $$ So, when 2.50 g of zinc reacts with excess aqueous hydrochloric acid, 0.0771 g of hydrogen gas is produced.

Key concepts

Chemical Reactions

Chemical reactions describe the process by which substances interact and transform into new products. In this exercise, the reaction involves zinc (Zn) and hydrochloric acid (HCl). This is a single displacement reaction, a type where an element displaces another in a compound, leading to the formation of a new product.

• Zinc, a metal, and hydrochloric acid, an aqueous solution, react to form zinc chloride (ZnCl₂) and hydrogen gas (H₂).
• The balanced chemical equation for this reaction is: \( \mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) \).

Chemical reactions like this one can be explored further using stoichiometry, which helps in predicting the amounts of products formed and reactants consumed.

Molar Mass Calculation

Molar mass is fundamental in stoichiometry, converting between mass and moles. It's the mass of one mole of a substance, expressed in grams per mole (g/mol). This concept is used to relate the mass of a chemical substance to the quantity in moles.

• To calculate the molar mass of zinc, we use its atomic mass of 65.38 g/mol.
• For hydrogen gas (H₂), with two hydrogen atoms, its molar mass is 2.02 g/mol.

The calculation of moles from mass involves the equation: \[\text{moles} = \frac{\text{mass of substance}}{\text{molar mass}}\]This conversion is critical in predicting product amounts by using the balanced reaction equation as a guide.

Hydrogen Gas Production

In this type of reaction, understanding how to calculate and predict hydrogen gas yield is crucial. Producing hydrogen gas involves using metals like zinc reacting with acids, which is a common laboratory practice.

• Starting with 2.50 g of zinc, we determine moles using its molar mass: \( 0.0382 \text{ mol of Zn} \).
• The stoichiometry of the reaction shows a 1:1 mole ratio between zinc and hydrogen gas.
• This means the moles of hydrogen gas produced equals the moles of zinc reacted: \( 0.0382 \text{ mol of H}_2 \).
• Finally, converting moles of hydrogen to mass involves multiplying by the molar mass of hydrogen, resulting in 0.0771 g of hydrogen gas.

Such calculations underline the importance of understanding stoichiometry and reactions to estimate gas production efficiently.