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Solution: 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

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

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.

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