Q. 8.73 - An Introduction to General, Organic, and Biological Chemistry

Question

A sample of Hydrogen$\left(H_2\right)$ gas at $127°C$ has a pressure of $2.00atm$. at final temperature, in degrees Celcius, will the pressure of the $H_2$ decreases to $0.25atm$, if  $V and n$ do not change?

Step-by-Step Solution

Answer

The final temperature of $H_2$ will be $-223°C$.

Step 1: Given Information

We have given the temperature is $127°C$ and pressure is $2.00atm$ of Hydrogen$\left(H_2\right)$.

Step 2: Simplify

According to the question, there will be no change in the amount of gas and the volume of the gas will also be constant.

Using combined gas law

$\frac{p_1{V}_1}{T_1}=\frac{p_2{V}_2}{T_2}$

We can see, the pressure is directly related to the temperature. 

So, 

$$\begin{gathered} T_2=\frac{P_2{T}_2}{P_1}=\frac{0.25atm\times 400K}{2atm} \\ {T}_2=50K \\ {T}_2=\left(50-273\right)°C=-223°C \end{gathered}$$