State Gay Lussac's law related to pressure and temperature of a gas. 3.2 g of sulphur when vaporised the sulphur vapour occupies a volume of 280.2 mL at STP. Determine the molecular formula of sulphur vapour under this condition. (S = 32) [1 + 2]

**OR**

Determine the volume of

Question

State Gay Lussac's law related to pressure and temperature of a gas. 3.2 g of sulphur when vaporised the sulphur vapour occupies a volume of 280.2 mL at STP. Determine the molecular formula of sulphur vapour under this condition. (S = 32) [1 + 2]

**OR**

Determine the volume of 2.2 g of carbon dioxide at 27°C and 570 mm Hg pressure.

Accepted Answer

>

> [!TLDR]
> Gay-Lussac's law relates pressure and temperature at constant volume; use the ideal-gas molar volume at STP to find the molar mass of the sulphur vapour, then divide by the atomic mass of S.
>
> **Gay-Lussac's Law:** at constant volume, the pressure of a fixed mass of gas is directly proportional to its absolute (Kelvin) temperature:
> $$P \propto T \quad (	ext{at constant } V, n) \quad \Rightarrow \quad \frac{P_1}{T_1} = \frac{P_2}{T_2}$$
>
> **Molecular formula calculation:**
>
> At STP, 1 mole of any ideal gas occupies $22{,}400$ mL ($22.4$ L).
>
> **Step 1 — Moles of sulphur vapour:**
> $$n = \frac{280.2\ 	ext{mL}}{22{,}400\ 	ext{mL mol}^{-1}} = 0.0125\ 	ext{mol}$$
>
> **Step 2 — Molar mass of the vapour:**
> $$M = \frac{	ext{mass}}{n} = \frac{3.2\ 	ext{g}}{0.0125\ 	ext{mol}} = 256\ 	ext{g mol}^{-1}$$
> …

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