At $\mathrm{T}(\mathrm{K})$, an ideal gas $(\mathrm{Z})$ present in $\mathrm{V}$ L flask exerted a pressure…

At $\mathrm{T}(\mathrm{K})$, an ideal gas $(\mathrm{Z})$ present in $\mathrm{V}$ L flask exerted a pressure of $16.4 \mathrm{~atm}$. Its concentration is $1 \mathrm{~mol} \mathrm{~L}^{-1}$. What is the value of $\mathrm{T}$ in $\mathrm{K}$ ?
  1. $100$
  2. $400$
  3. $300$
  4. $200$

Solution

$\begin{aligned} & \text {} \mathrm{pV}=\mathrm{nRT} \Rightarrow \mathrm{p}=\frac{\mathrm{n}}{\mathrm{V}} \mathrm{RT}=\mathrm{CRT} \\ & \begin{aligned} \Rightarrow \mathrm{T} & =\frac{\mathrm{P}}{\mathrm{CR}}=\frac{16.4 \mathrm{~atm}}{\left(1 \mathrm{~mol} \mathrm{~L}^{-1}\right)\left(0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}{ }^{-1} \mathrm{~K}^{-1}\right)} \\ & =200 \mathrm{~K}\end{aligned}\end{aligned}$

Asked in: AP EAMCET 2023 (17 May Shift 1)

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