Modern pennies are composed of zinc coated with copper. A student determines the mass of a penny to be 2.482 g and then makes several scratches in the copper coating (to expose the underlying zinc). The student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the HCl (the copper remains undissolved): Zn(s) + 2 HCl(aq)¡ H2( g) + ZnCl2(aq) The student collects the hydrogen produced over water at 25 °C. The collected gas occupies a volume of 0.899 L at a total pressure of 791 mmHg. Calculate the percent zinc (by mass) in the penny. (Assume that all the Zn in the penny dissolves.)

Verified step by step guidance

1. Determine the partial pressure of hydrogen gas by subtracting the vapor pressure of water at 25 °C from the total pressure. Use the vapor pressure of water at 25 °C, which is 23.8 mmHg.
2. Convert the partial pressure of hydrogen gas from mmHg to atm using the conversion factor: 1 atm = 760 mmHg.
3. Use the ideal gas law, PV = nRT, to calculate the number of moles of hydrogen gas (n). Use R = 0.0821 L·atm/mol·K and convert the temperature to Kelvin by adding 273.15 to the Celsius temperature.
4. Use the stoichiometry of the balanced chemical equation to determine the moles of zinc that reacted. Since 1 mole of Zn produces 1 mole of H2, the moles of Zn are equal to the moles of H2.
5. Calculate the mass of zinc using the moles of zinc and the molar mass of zinc (65.38 g/mol). Then, calculate the percent zinc by mass in the penny using the formula: (mass of Zn / total mass of penny) * 100%.

Key Concepts

Stoichiometry

Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the relationships between the amounts of substances consumed and produced. In this case, stoichiometry will help relate the volume of hydrogen gas produced to the amount of zinc that reacted with hydrochloric acid.

Gas Laws

Gas laws describe the behavior of gases under various conditions of temperature and pressure. The Ideal Gas Law (PV=nRT) is particularly useful for calculating the number of moles of gas produced in a reaction. In this scenario, the total pressure of the collected hydrogen gas must be adjusted for water vapor pressure to find the effective pressure of the hydrogen, which is essential for determining the moles of hydrogen produced.

Percent Composition

Percent composition is a way to express the mass percentage of each element in a compound or mixture. It is calculated by dividing the mass of the element by the total mass of the compound and multiplying by 100. In this problem, calculating the percent zinc in the penny requires determining the mass of zinc that reacted and comparing it to the total mass of the penny.