The volume of a gas is $4 \mathrm{dm}^3$ at $0^{\circ} \mathrm{C}$. Calculate new volume at constant…

The volume of a gas is $4 \mathrm{dm}^3$ at $0^{\circ} \mathrm{C}$. Calculate new volume at constant pressure when the temperature is increased by $10^{\circ} \mathrm{C}$.
  1. $2.07 \mathrm{dm}^3$
  2. $3.21 \mathrm{dm}^3$
  3. $4.14 \mathrm{dm}^3$
  4. $6.54 \mathrm{dm}^3$

Solution

According to Charles' law, $\begin{aligned} & \frac{\mathrm{V}_1}{\mathrm{~T}_1}=\frac{\mathrm{V}_2}{\mathrm{~T}_2} \text { (at constant } \mathrm{P} \text { and } \mathrm{n} \text { ) } \\ & \mathrm{T}_1=0{ }^{\circ} \mathrm{C}=273 \mathrm{~K} \\ & \mathrm{~T}_2=10^{\circ} \mathrm{C}=283 \mathrm{~K} \\ & \frac{4 \mathrm{dm}^3}{273 \mathrm{~K}}=\frac{\mathrm{V}_2}{283 \mathrm{~K}} \\ & \mathrm{~V}_2=\frac{4 \times 283}{273}=4.1465 \mathrm{dm}^3 \end{aligned}$

Asked in: MHT CET 2023 (13 May Shift 1)

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