Ideal Gas Equation

Rarely Tested

Ideal Gas Equation

### Formula:

$$PV=nRT$$

### Terminologies:

- P β†’ Pressure exerted by the gas.

- V β†’ Volume occupied by the gas.

- n β†’ Number of moles of gas.

- R β†’ Universal gas constant.

- T β†’ Absolute temperature in Kelvin.

- Ideal Gas β†’ Hypothetical gas obeying gas laws perfectly.

### Usage:

- Used to relate pressure, volume, temperature, and number of moles of a gas.

Question 1

Two cylinders, both fitted with frictionless pistons, are filled with mixtures of $$\mathrm{He}$$ and $$\mathrm{Ar}$$ gases. In the first cylinder, the masses of $$\mathrm{He}$$ and $$\mathrm{Ar}$$ are $$m_1$$ and $$m_2$$, respectively. In the second cylinder, the masses of $$\mathrm{He}$$ and $$\mathrm{Ar}$$ are $$m_2$$ and $$m_1$$, respectively. The molar mass of $$\mathrm{Ar}$$ is $$10$$ times the molar mass of $$\mathrm{He}$$. The external pressure applied by the piston on the first cylinder needs to be $$5$$ times that on the second cylinder so that the volume of the gas mixtures in both the cylinders are equal at the same temperature. Assuming $$\mathrm{He}$$ and $$\mathrm{Ar}$$ behave like ideal gases, the value of $$(m_1/m_2)$$ is ___.

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