Question

A sample of hydrogen gas occupies a volume of 300 ml at 1.2 bar pressure and 25 degree C. Calculate its volume at 0.45 bar pressure and 700 C

Answer 1

2612 mL

Step-by-step explanation

Given:

The initial volume, V₁ = 300 mL

The initial pressure, P₁ = 1.2 bar

The initial temperature, T₁ = 25⁰C = (25⁰C + 273) = 298 K

The final pressure, P₂ = 0.45 bar

The final temperature, T₂ = 700⁰C = (700⁰C + 273) = 973 K

What to find:

The final volume, V₂ of the gas at 0.45 bar pressure and 700⁰C.

Step-by-step solution:

The question is a volume, pressure, and temperature relationship.

The final volume, V₂ of the gas at 0.45 bar pressure and 700⁰C can be calculated using the Combine gas law equation.

`\begin{gathered} (P_1V_1)/(T_1)=(P_2V_2)/(T_2) \\ \\ V_2=(P_1V_1T_2)/(T_1P_2) \end{gathered}`

Substituting the values of the parameters into the formula

`\begin{gathered} V_2=\frac{1.2\text{ }bar*300\text{ }mL*973\text{ }K}{298\text{ }K*0.45\text{ }bar} \\ \\ V_2=\frac{350280\text{ }mL}{134.1} \\ \\ V_2=2612\text{ }mL \end{gathered}`

Hence, the volume of the hydrogen gas sample at 0.45 bar pressure and 700⁰C is 2612 mL.