The correct option in which the density of argon (Atomic mass = 40) is highest:

Question

Accepted Answer

C. 1. Start from the **ideal gas equation**, since it relates pressure, volume, and temperature to the amount of gas:
$$
PV=nRT
$$

2. Since the number of moles $n=\frac{w}{M}$ (mass divided by molar mass), substitute this in:
$$
PV=\frac{w}{M}RT
$$

3. Rearranging to get an expression for **density** $ho=\frac{w}{V}$:
$$
ho=\frac{PM}{RT}
$$

4. This tells us density is **directly proportional to pressure** and **inversely proportional to temperature**, since $M$ and $R$ are constants for a given gas.

So, to get the **highest density**, we need the option with the **highest pressure** and the **lowest temperature**.

5. Compare all four options:

- STP: $T=273	ext{ K}$, $P=1	ext{ atm}$
- 0°C, 2 atm: $T=273	ext{ K}$, $P=2	ext{ atm}$
- 0°C, 4 atm: $T=273	ext{ K}$, $P=4	ext{ atm}$
- 273°C, 4 atm: $T=546	ext{ K}$, $P=4	ext{ atm}$

6. Among these, **0°C, 4 atm** has the highest pressure at the lowest possible temperature (273 K), since the last option has the same pressure but a much higher temperature (546 K), which lowers its density.

Hence, the answer is **C**.