Final answer:
To calculate the mass of magnesium needed, we need to use the ideal gas law to find the moles of hydrogen gas produced and then use stoichiometry to find the equivalent moles of magnesium required.
Step-by-step explanation:
The student is asking how to calculate the mass of magnesium needed to produce a certain volume of hydrogen gas from a reaction with hydrochloric acid. The reaction is represented by: Mg(s) + 2 HCl(aq) → MgCl2(aq) + H2(g).
To solve this problem, we need to use the ideal gas law to find out how many moles of hydrogen gas (H2) are produced, and then relate this back to the amount of magnesium (Mg) required using stoichiometry.
Step-by-step Solution
- Convert the volume of hydrogen gas (H2) to liters.
- Use the ideal gas law (PV=nRT) to calculate the number of moles of H2 produced, where P is the pressure in atmospheres, V is the volume in liters, n is the number of moles, R is the gas constant (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
- Convert the pressure from mmHg to atm by dividing by 760.
- Convert the temperature from °C to Kelvin by adding 273.15.
- Use stoichiometry to convert moles of H2 to moles of Mg; since one mole of Mg produces one mole of H2, the moles are equal.
- Finally, calculate the mass of Mg required by multiplying the moles of Mg by its molar mass (24.305 g/mol).