# A mixture of four gases exerts a total pressure of 860 mmHg. Gases A and B each exert 220 mmHg. Gas C exerts 110 mmHg. What pressure is exerted by gas D?

May 21, 2016

$\text{310 mmHg}$

#### Explanation:

All you have to do here in order to figure out the pressure exerted by gas $\text{D}$ is use Dalton's Law of Partial Pressures.

In essence, Dalton's Law of Partial Pressures states that the total pressure exerted by a mixture of gases will be equal to the sum of the partial pressure each constituent of the mixture exerts in the same volume and under the same conditions for pressure and temperature.

color(blue)(|bar(ul(color(blue)(P_"total" = sum_i P_icolor(white)(a/a)|)))

In your case, four gases labeled $\text{A}$, $\text{B}$, $\text{C}$, and $\text{D}$ are placed in a container. The pressure of the gaseous mixture is said to be equal to $\text{860 mmHg}$.

This means that the partial pressures of the four gases must add up to give $\text{860 mmHg}$.

You will thus have

${P}_{\text{total}} = {P}_{A} + {P}_{B} + {P}_{C} + {P}_{D}$

This means that the partial pressure of gas $\text{D}$ will be equal to

P_D = "860 mmHg" - ( ${\overbrace{\text{220 mmHg")^(color(blue)(P_A)) + overbrace("220 mmHg")^(color(red)(P_B)) + overbrace("110 mmHg}}}^{\textcolor{b r o w n}{{P}_{C}}}$ )

P_D = "860 mmHg" - "550 mm Hg" = color(green)(|bar(ul(color(white)(a/a)"310 mmHg"color(white)(a/a)|)))