Question

Heyy.. I Need Some Help Pls..

The gas in a cylinder has a volume of 3 liters at a pressure of 111 kPa. The pressure of the gas is increased to 221 kPa. Assuming the temperature remains constant, what would the new volume be?

Answer 1

There are these gas laws that relate the parameters of pressure (P), volume (V), temperature (T) and amount of gas (in moles, n), when combined, they are known as the ideal gas law:

\(\sf \huge PV=nRT\)

R is the gas constant, btw.

When you have a question asking you to compare two scenarios (i.e. two systems) you can use the ideal gas law to figure out what the unknown parameter is.

We equate the two systems: \(\sf \underbrace{\dfrac{P_1V_1}{n_1RT_1}}_{system~1}=\underbrace{\dfrac{P_2V_2}{n_2RT_2}}_{system~2}\)

Now we omit what remains constant (T, n and R) and we're left with:

\(\sf P_1V_1=P_2V_2\)

Now your question asks to find the volume when the pressure is increased (to 221 kPa).

system 1: P = 111 kPa, V = 3 L

system 2: P = 221 kPa, V = ?

Solving for \(V_2\): \(\sf V_2=\dfrac{P_1V_1}{P_2}=\dfrac{3~L*111~kPa}{221~kPa}=1.506~L\)


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So in summary, for these questions use: \(\sf \dfrac{P_1V_1}{n_1T_1}=\dfrac{P_2V_2}{n_2T_2}\)

(Note R is omitted from this because it's a constant)

Omit from the equation what remains constant, solve for the unknown and plug in your variables.