Question

A five-fold increase in the mass of a gas would result in a five-fold _______ in pressure.

Answer 1

If the gas is ideal while volume and temperature stay unchanged, there would be a five-fold increase in the pressure of this gas.

Step-by-step explanation:

Let
`V` denote the volume of this gas, let
`P` denote the pressure of the gas, let
`n` denote the number of particles in this gas, let
`T` denote the temperature of this gas, and let
`R` denote the ideal gas constant.

If this gas is an ideal gas, it would satisfy the ideal gas law:

`P\, V = n\, R\, T`.

Assuming that this gas is uniform. The mass of this gas will be directly proportional to the number of particles
`n` in this gas. Hence, a five-fold increase in the mass of this will increase the number of particles in this gas by five folds.

Rearrange this equation to separate pressure
`P` from the number of particles in this gas
`n`:

`\begin{aligned} P &= \left((R\, T)/(V)\right) \, n\end{aligned}`.

In other words, if the temperature and volume of this gas stays the same, the pressure
`P` of this gas will be proportional to the number of particles
`n` in this gas. Thus, the five-fold increase in the number of particles (from a five-fold increase in mass) will increase the pressure of this gas by five folds.