Question

A sample of hydrogen gas has a density of ___ g/L at a pressure of 0.799 atm and a temperature of 47 °C. Assume ideal behavior.

Answer 1

Answer: The density of the given sample of hydrogen gas is 0.061 g/L

Step-by-step explanation:

Assuming ideal gas behavior, the equation follows:

PV = nRT

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}`

Rearranging the above equation:

`P=(m)/(M)(RT)/(V)`

We know that:

`\text{Density}=\frac{\text{Mass}}{\text{Volume}}`

Rearranging the above equation:

`P=(dRT)/(M)` ......(1)

We are given:

P = pressure of the gas = 0.799 atm

d = density of hydrogen gas = ?

R = Gas constant =
`0.0821\text{ L . atm }mol^(-1)K^(-1)`

T = temperature of the gas =
`47^oC=[47+273]K=320K`

M = molar mass of hydrogen gas = 2 g/mol

Putting values in equation 1, we get:

`0.799atm=\frac{d* 0.0821\text{ L.atm }mol^(-1)K^(-1)* 320K}{2g/mol}\\\\d=(0.799* 2)/(0.0821* 320)=0.061g/L`

Hence, the density of the given sample of hydrogen gas is 0.061 g/L