Question

At constant temperature, the pressure of a sample of gas is inversely proportional to its volume. I have some oxygen in a 2.28 liter container with a pressure of 5 kPa. If I move all of it to a 5.7 liter container at the same temperature, what will the new pressure be in kPa?

Answer 1

The new pressure is 2 Kpa

Solution:

At constant temperature, the pressure of a sample of gas is inversely proportional to its volume

Therefore,

`\text{ pressure of a sample of gas} \propto \frac{1}{\text{volume}}`

Let "p" be the pressure of sample gas

Let "v" be the volume

Then we get,

`p \propto (1)/(v)\\\\p = k * (1)/(v)\\\\p = (k)/(v) ---------- eqn 1`

Where, "k" is the constant of proportionality

I have some oxygen in a 2.28 liter container with a pressure of 5 kPa

Substitute v = 2.28 and p = 5 in eqn 1

`5 = (k)/(2.28)\\\\k = 5 * 2.28\\\\k = 11.4`

I move all of it to a 5.7 liter container at the same temperature

Substitute k = 11.4 and v = 5.7 in eqn 1

`p = (11.4)/(5.7)\\\\p = 2`

Thus new pressure is 2 kPa