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:
\(x_1=\frac{P_1}{P_{\text {total }}}\)