Question

The amount of Zinc (atomic weight \(=65\) ) necessary to produce \(224 \mathrm{~mL}\) of \(\mathrm{H}_{2}\) by the reaction with an acid will be: (a) \(0.65 \mathrm{~g}\) (b) \(7.6 \mathrm{~g}\) (c) \(6.5 \mathrm{~g}\) (d) \(8.5 \mathrm{~g}\)

Short answer

The answer is (a) 0.65 g of Zinc.

Step-by-step solution

Write the Balanced Chemical Equation

The reaction of zinc with an acid that releases hydrogen gas can be written as: \[ \text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \]This balanced equation shows that 1 mole of Zn produces 1 mole of \(\text{H}_2\).

Calculate Moles of Hydrogen Gas

Use the Ideal Gas Law to determine the moles of \(\text{H}_2\). At STP (standard temperature and pressure), 1 mole of any gas occupies \(22.4 \text{ L}\). Convert \(224 \text{ mL}\) to liters (\(0.224\text{ L}\)).\[ \frac{0.224 \text{ L}}{22.4 \text{ L/mol}} = 0.01 \text{ mol} \]

Calculate Moles of Zinc Required

From the balanced equation, \(1 \text{ mol Zn}\) produces \(1 \text{ mol } \text{H}_2\). Therefore, \(0.01 \text{ mol } \text{Zn}\) is required to produce \(0.01 \text{ mol } \text{H}_2\).

Calculate Mass of Zinc Required

The atomic weight of zinc is \(65 \text{ g/mol}\). Calculate the mass of zinc:\[ 0.01 \text{ mol} \times 65 \text{ g/mol} = 0.65 \text{ g} \]

Choose the Correct Answer

The amount of zinc required to produce \(224 \text{ mL}\) of \(\text{H}_2\) is \(0.65 \text{ g}\). The correct answer is: (a) \(0.65 \text{ g}\).

Key concepts

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry used to relate the properties of gases. It connects the pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas with the gas constant (R). The equation is expressed as:\[ PV = nRT \]This law helps in understanding how gases behave under various conditions. In the context of the zinc reaction with an acid, we use the Ideal Gas Law to find out how many moles of hydrogen gas are produced.

• Standard Temperature and Pressure (STP) is often used as a reference, where the temperature is 273.15 K (0°C) and pressure is 1 atm.
• At STP, one mole of any ideal gas occupies a volume of 22.4 liters.

To calculate the moles of hydrogen gas from its given volume at STP, we convert the volume from milliliters to liters and then divide by the molar volume (22.4 L/mol). This gives us the moles of hydrogen gas, which is crucial for the next steps in the calculation.

Stoichiometry

Stoichiometry is the section of chemistry that deals with the quantitative relationships between the reactants and products in a chemical reaction. The balanced chemical equation provides a wealth of information about these relationships. For the reaction between zinc and hydrochloric acid:\[ \text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \]This shows a 1:1 ratio between zinc and hydrogen gas. Using stoichiometry, we can infer how much zinc is needed to produce a specific amount of hydrogen gas. Here's how it works:

• From the reaction, 1 mole of zinc produces 1 mole of hydrogen gas.
• If we calculate the moles of hydrogen gas (using the Ideal Gas Law), stoichiometry tells us the same number of moles of zinc is needed.

This methodology allows us to accurately determine the mass of zinc required by linking its moles to hydrogen via their ratio in the balanced equation.

Chemical Equations

Chemical equations are essential for representing chemical reactions. They show how reactants transform into products. The first step in solving any problem involving chemistry calculations is to write a balanced chemical equation.In the zinc reaction with hydrochloric acid:\[ \text{Zn} + 2\text{HCl} \rightarrow \text{ZnCl}_2 + \text{H}_2 \]

• This balanced equation tells us the proportions in which the substances react.
• It's essential to balance the chemical equation prior to making any calculations because it ensures the law of conservation of mass is adhered to.

The equation must have the same number of atoms of each element on both sides. This guarantees that no atoms are lost or gained, preparing us to accurately gauge the stoichiometry of the reaction.