Question

What is the density of a sample of hydrogen gas (H₂) that exerts 2.85 atm of pressure at 225K?

Answer 1

At 2.85 atm and 225K, the density of hydrogen gas (
`\(H_2\)`) is approximately 31.3 g/L using the ideal gas law.

To find the density of a gas using the ideal gas law (PV = nRT), you'll need the molar mass of hydrogen (
`\(H_2\)`) and the ideal gas constant provided.

Given:

Pressure (P) = 2.85 atm

Temperature (T) = 225 K

Gas constant (R) = 0.08206 L atm / (mol K)

Molar mass of hydrogen (
`\(H_2\)`) = 2 g/mol

The ideal gas law equation is PV = nRT. We want to rearrange it to solve for density (d) using the formula:

`\[d = \frac{\text{molar mass} * P}{R * T}\]`

First, convert the pressure unit to Pa (Pascals) since the ideal gas constant is in the units of L atm/mol K.

`\(1 \, \text{atm} = 101325 \, \text{Pa}\).`

`\[2.85 \, \text{atm} = 2.85 * 101325 \, \text{Pa} = 289103.25 \, \text{Pa}\]`

Now, plug the values into the formula:

`\[d = \frac{2 \, \text{g/mol} * 289103.25 \, \text{Pa}}{0.08206 \, \text{L atm/mol K} * 225 \, \text{K}}\]`

Solving this gives:

`\[d \approx (578206.5)/(18463.5) \approx 31.34 \, \text{g/L}\]`

Rounded to three significant figures, the density of the hydrogen gas sample at the given conditions is approximately
`\(31.3 \, \text{g/L}\)`.

Question:

What is the density of a sample of hydrogen gas (H2) that exerts 2.85 atm of pressure at 225K?

• Use 0.08206L atmmol K for the ideal gas constant.
• Round the answer to three significant figures.