Question

A 0.539 g sample of a metal, M, reacts completely with sulfuric acid according to the reaction M(s)+H2SO4(aq)⟶MSO4(aq)+H2(g) A volume of 249 mL of hydrogen gas is collected over water; the water level in the collecting vessel is the same as the outside level. Atmospheric pressure is 1.0079 bar and the temperature is 25 °C. The vapor pressure of water at 25 °C is 0.03167 bar. Calculate the molar mass of the metal.

Answer 1

Answer:

The molar mass of the metal is 54.9 g/mol.

Explanation:

When we work with gases collected over water, the total pressure (atmospheric pressure) is equal to the sum of the vapor pressure of water and the pressure of the gas.

Patm = Pwater + PH₂

PH₂ = Patm - Pwater = 1.0079 bar - 0.03167 bar = 0.9762 bar

The pressure of H₂ is:

$0.9762bar.\frac{1atm}{1.013bar} =0.9637atm$

The absolute temperature is:

K = °C + 273 = 25°C + 273 = 298 K

We can calculate the moles of H₂ using the ideal gas equation.

$P.V=n.R.T\\n=\frac{P.V}{R.T} =\frac{0.9637atm \times 0.249L }{(0.08206atm.L/mol.K)\times298K} =9.81 \times 10^{-3} mol$

Let's consider the following balanced equation.

M(s) + H₂SO₄(aq) ⟶ MSO₄(aq) + H₂(g)

The molar ratio of M:H₂ is 1:1. So, 9.81  × 10⁻³ moles of M reacted. The molar mass of the metal is:

$\frac{0.539g}{9.81 \times 10^{-3} mol} =54.9g/mol$