Question

What is the total pressure of a mixture that contains 50% nitrogen at 1.7 atm, 23% oxygen at 1.1 atm, 12% argon at 0.7atm, 10% methane at 0.5 atm, and 5% water vapor at 0.2 atm?A. 1.247 atmB. 4.2 atmC. 0.13 atmD. 0.85 atm

Answer 1

A. 1.247 atm.

Step-by-step explanation:

The Behavior of Gases => Dalton's Law of Partial Pressures.

The partial pressure of a gas is the contribution that gas makes to the total pressure when the gas is part of a mixture. Dalton's law of partial pressures states that the total pressure of a mixture of gases is equal to the sum of all of the partial pressures of the component gases and it can be expressed as follows:

`P_(total)=P_1+P_2+...`

In the statement, they are telling us that we have the pressures of various gases in different proportions as percentages. Remember that percentages can be written as decimals by dividing the percentages by 100: 50 % is 0.5, 23% is 0.23, and so on.

So first, let's find the partial pressures of all the gases multiplying the percentage as decimals with the given pressure:

`\begin{gathered} P_(nitrogen)=0.5\cdot1.7\text{ atm=0.85 atm,} \\ \\ P_(oxygen)=0.23\cdot1.1\text{ atm=0.253 atm,} \\ \\ P_(argon)=0.12\cdot0.7\text{ atm=0.084 atm,} \\ \\ P_(methane)=0.1\cdot0.5\text{ }atm=0.05\text{ atm,} \\ \\ P_{water\text{ vapor}}=0.05\cdot0.2\text{ atm=0.01 atm.} \end{gathered}`

Now that we found the partial pressures, we can obtain the total pressure using the initial formula, like this:

`\begin{gathered} P_(total)=P_(nitrogen)+P_(oxygen)+P_(argon)+P_(methane)+P_{water\text{ vapor}}, \\ \\ P_(total)=(0.85+0.253+0.084+0.05+0.01)atm, \\ \\ P_(total)=1.247\text{ atm.} \end{gathered}`

The answer would be that the total pressure is A. 1.247 atm.