A 25-L container holds ideal hydrogen (H₂)gas at a gauge pressure of 0.25 atm and a temperature of 0°C.What mass of hydrogen gas is in this container? The ATOMIC mass of hydrogen is 1.0 g/mol,the ideal gas constant is R = 8.314 J/mol ∙ K = 0.0821 L ∙ atm/mol ∙ K,and 1.00 atm = 101 kPa. A)1.4 g B)2.8 g C)4.2 g D)5.6 g E)6.3 g

Question

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First, convert the gauge pressure to absolute pressure by adding atmospheric pressure (1 atm) to the gauge pressure (0.25 atm), giving 1.25 atm. Use the ideal gas law, PV = nRT, where P is the pressure in atm (1.25 atm), V is the volume in liters (25 L), R is the ideal gas constant (0.0821 L∙atm/mol∙K), and T is the temperature in Kelvin (273 K, since 0°C = 273 K). Solve for n (moles of hydrogen), then multiply by the molar mass of hydrogen (2.0 g/mol for H2) to find the mass. Calculation: n = PV/RT = (1.25 atm * 25 L) / (0.0821 L∙atm/mol∙K * 273 K) ≈ 1.4 mol, and mass = n * molar mass = 1.4 mol * 2.0 g/mol = 2.8 g.

A 25-L Container Holds Ideal Hydrogen (H2)gas at a Gauge

A 25-L Container Holds Ideal Hydrogen (H₂)gas at a Gauge