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:
[tex]0.9762bar.\frac{1atm}{1.013bar} =0.9637atm[/tex]
The absolute temperature is:
K = °C + 273 = 25°C + 273 = 298 K
We can calculate the moles of H₂ using the ideal gas equation.
[tex]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[/tex]
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:
[tex]\frac{0.539g}{9.81 \times 10^{-3} mol} =54.9g/mol[/tex]
The molar mass of the metal that reacted with sulfuric acid to liberate 249 mL of hydrogen gas is 55 g/mol
n = PV / RT
n = (0.97623 × 0.249) / (8.314×10¯² × 298)
n = 0.0098 mole
Balanced equation
M(s) + H₂SO₄(aq) —> MSO₄(aq) + H₂(g)
From the balanced equation above,
1 mole of M reacted to produce 1 mole of H₂.
Therefore,
0.0098 mole of M will also react to produce 0.0098 mole of H₂
Molar mass = mass / mole
Molar mass of metal = 0.539 / 0.0098
Molar mass of metal = 55 g/mol
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