# Problem: Calcium perbromate, Ca(BrO4)2 (m.w.= 327.9 g/mol) decomposes upon heating to release oxygen gas according to the equation below. A sample containing Ca(BrO4)2 is heated and the gas produced collected by downward displacement of water at 50.0°C. The total volume of gas collected was 438.0 ml at an atmospheric pressure of 680 torr. The vapor pressure of water at 50.0°C is 92.5 torr.Ca(BrO4)2 (s) → CaBr2 (s) + 4 O2 (g)a.) Calculate the number of grams of Ca(BrO 4)2 in the original sample. b.) Calculate the mole fraction of oxygen in the collected gas mixture

###### FREE Expert Solution

For the given decomposition reaction of calcium perbromate, we´re asked to determine the number of grams of Ca(BrO4)2 in the original sample, and the mole fraction of oxygen in the collected gas mixture.

When a gas is collected in a container by water displacement, the container has two gases

the collected gas and water vapor.

According to Dalton’s Law, in a container of unreactive gases, the total pressure of the container is the sum of the partial pressures of the individual gases.

In this problem, Dalton’s Law adopts the following form:

$\overline{){{\mathbf{P}}}_{{\mathbf{T}}}{\mathbf{=}}{{\mathbf{P}}}_{{\mathbf{g}}}{\mathbf{+}}{{\mathbf{P}}}_{{\mathbf{v}}}}$

Where

PT = total pressure of the container, atm or torr

Pg = partial pressure of the collected gas, atm or torr

Pv = partial vapor pressure of water, atm or torr

The problem can be solved in 4 steps:

Step 1: Calculate the pressure of the collected oxygen.

###### Problem Details

Calcium perbromate, Ca(BrO4)2 (m.w.= 327.9 g/mol) decomposes upon heating to release oxygen gas according to the equation below. A sample containing Ca(BrO4)2 is heated and the gas produced collected by downward displacement of water at 50.0°C. The total volume of gas collected was 438.0 ml at an atmospheric pressure of 680 torr. The vapor pressure of water at 50.0°C is 92.5 torr.

Ca(BrO4)2 (s) → CaBr2 (s) + 4 O2 (g)

a.) Calculate the number of grams of Ca(BrO 4)2 in the original sample.

b.) Calculate the mole fraction of oxygen in the collected gas mixture