If $P_1$ partial pressure of a gas and $x_1$ is its mole fraction in a mixture, then correct relation…

If $P_1$ partial pressure of a gas and $x_1$ is its mole fraction in a mixture, then correct relation between $P_1$ and $x_1$ is
  1. $\quad \mathrm{P}_{\text {total }}=\mathrm{P}_1 \mathrm{X}_1$
  2. $\quad \mathrm{x}_1=\frac{\mathrm{P}_1}{\mathrm{P}_{\text {total }}}$
  3. $\quad \mathrm{P}_{\text {total }}=1-\mathrm{P}_1 \mathrm{x}_1$
  4. $\quad \mathrm{P}_{\text {total }}=\mathrm{P}_1\left(1-\mathrm{x}_1\right)$

Solution

The correct relation between the partial pressure of a gas \(\left(P_1\right)\) and its mole fraction \(\left(x_1\right)\) in a mixture is given by Dalton's Law of Partial Pressures. According to this law, the partial pressure of a gas in a mixture is proportional to its mole fraction and the total pressure of the mixture. The expression can be written as: \(P_1=x_1 \cdot P_{\text {total }}\) From this relationship, we can derive the mole fraction as: \(x_1=\frac{P_1}{P_{\text {total }}}\) This corresponds to Option B: \(x_1=\frac{P_1}{P_{\text {total }}}\)

Asked in: MHT CET 2024 (11 May Shift 2)

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