A sample of hydrogen gas has a density of ____ g/L at a pressure of 0.965 atm and a temperature of 51.0 °C. Assume ideal behavior.

Answer 1

Let's start from the ideal gas law:

PV = nRT

Density = mass / volume. While the ideal gas equation includes volume (V), how can we get the mass of the gas? Well, we know that the mass of a sample is related to the number of moles (n) present. By using the molar mass of the gas, we can convert moles to mass. Since our gas is hydrogen, the molar mass of the gas is 2.016 g/mol (don't forget that hydrogen gas is diatomic!)

n = m/M ; n = moles, m = mass (g), M = molar mass (g/mol)

If we substitute "m/M" in for "n" into our ideal gas equation, we get:

PV = (m/M) RT

We can now use algebra to rearrange this equation to solve for m/V (density).

m/V = PM / RT

m/V = (.965 atm)(2.016 g/mol)/(0.0821 L*atm/mol*K)(324 K)

m/V = 0.0731 g/L

Answer 2

ρ_i = M_iP/RT where M_i is the molar mass in grams and R is the usual .0821 liter-atm/mole-Kelvin. The density will be in grams/liter.