Question

If John has 2.3 liters of gas held at a pressure of 8.2 atm and a temperature of 540 K, what will be the volume of the gas if I decrease the pressure to 3.8 atm and decrease the temperature to 310 K?

Answer 1

The final volume of the gas is 2.8 liters

Step-by-step explanation

Given that;

The initial volume of the gas is 2.3 liters

The initial temperature of the gas is 540K

The initial pressure of the gas is 8.2 atm

The final temperature of the gas is 310K

The final pressure of the gas is 3.8 atm

Follow the steps below to find the final volume of the gas

Step 1; Apply the general gas law equation

`\text{ }(P1V1)/(T1)\text{ }=\text{ }\frac{P2\text{ V2}}{T2}`

Where

• P1 is the initial pressure

,

• V1 is the initial volume

,

• T1 is the initial temperature

,

• P2 is the final pressure

,

• T2 is the final temperature

,

• V2 is the final volume

Step 2; substitute the given data into the formula in step 1 to find the final volume of the gas

`\begin{gathered} \text{ }\frac{8.2*\text{ 2.3}}{540}\text{ }=\text{ }(3.8* V2)/(310) \\ \text{ cross multiply} \\ \text{ 3.8}* V2*540\text{ }=\text{ 8.2}*2.3*310 \\ 2052V2\text{ }=\text{ 5846.6} \\ \text{ Divide both sides by 2052} \\ \text{ }\frac{\cancel{2052}V2}{\cancel{2052}}=(5846.6)/(2052) \\ \text{ V2 }=\text{ 2.8 liters} \end{gathered}`

Therefore, the final volume of the gas is 2.8 liters