# A given mass of oxygen occupies 200 ml when the pressure is 400 mm of Hg. What volume will the gas occupy when the pressure is raised to 200 mmHg, provided the temperature remains constant?

Apr 18, 2017

At constant temperature, ${P}_{1} {V}_{1} = {P}_{2} {V}_{2}$........${V}_{2} = 400 \cdot m L$

#### Explanation:

Now we know that $1 \cdot a t m$ pressure will support of column of mercury $760 \cdot m m$ high. A pressure of LESS than one atmosphere will support a column of mercury LESS than this length.

So here ${P}_{1} = \frac{400 \cdot m m}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1} = 0.526 \cdot a t m$

And ${P}_{2} = \frac{200 \cdot m m}{760 \cdot m m \cdot H g \cdot a t {m}^{-} 1} = 0.263 \cdot a t m$

So ${P}_{2}$ was half of ${P}_{1}$.

And we plug in the numbers, and expect reasonably that ${V}_{2}$ WILL INCREASE, given that we reduce the pressure, the force per unit area on the gas:

${V}_{2} = \frac{0.526 \cdot a t m \times 200 \cdot m L}{0.263 \cdot a t m} = 400 \cdot m L$