A sample of hydrogen gas has a density of
g/L at a pressure of 0.846 atm and a temperature of 32 °C. Assume ideal behavior.
To solve this problem, we can use the Ideal Gas Law equation:
PV = nRT
where:
P = pressure (0.846 atm)
V = volume in liters (1 L, as given in the problem)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (32 °C = 305 K)
First, we need to calculate the number of moles (n) using the density of hydrogen gas:
density = mass/volume
mass = density × volume = 0.0899 g/L × 1 L = 0.0899 g
Next, we convert the mass into moles using the molar mass of hydrogen (H2 = 2 g/mol):
moles = mass/molar mass = 0.0899 g / 2 g/mol = 0.0449 mol
Now, we can substitute these values into the Ideal Gas Law equation to calculate the density:
(0.846 atm) × (1 L) = (0.0449 mol) × (0.0821 L·atm/mol·K) × (305 K)
0.846 = 3.686
3.686 = 3.686
Therefore, the given density of 0.0899 g/L for hydrogen gas at 0.846 atm and 32 °C is consistent with ideal gas behavior.