Question

A mixture of three gases, A, B, and C, is at a total pressure of 6.11 atm. The partial pressure of gas A is 1.68 atm; that of gas B is 3.89 atm. What is the partial pressure of gas C?

Short answer

The partial pressure of gas C is 0.54 atm.

Step-by-step solution

- Understand the Problem

We need to find the partial pressure of gas C in a mixture of three gases (A, B, and C) given the total pressure and partial pressures of gases A and B.

- Write Down Given Data

We have the total pressure \(P_{total} = 6.11\ atm\) and the partial pressures of gases A and B as \(P_A = 1.68 \ atm\) and \(P_B = 3.89 \ atm\), respectively.

- Apply Dalton's Law of Partial Pressures

Dalton's Law states that the total pressure exerted by a mixture of non-reacting gases is equal to the sum of the partial pressures of individual gases. Thus, \[P_{total} = P_A + P_B + P_C \]

- Substitute Known Values

Substitute the given values into the equation: \(6.11 = 1.68 + 3.89 + P_C \)

- Solve for Partial Pressure of Gas C

Now, isolate \(P_C\) to find its value: \[P_C = 6.11 - 1.68 - 3.89 \]

- Perform the Calculation

Calculate the value: \[P_C = 6.11 - 1.68 - 3.89 = 0.54 \ atm\]

Key concepts

Partial Pressure

When dealing with gas mixtures, understanding partial pressure is crucial. Partial pressure is the pressure each gas in a mixture would exert if it were alone in the container. Each gas contributes to the total pressure in proportion to its amount. The sum of all partial pressures in the mixture equals the total pressure. This concept helps us determine individual gas pressures in mixtures. In the provided exercise, the mixture involves gases A, B, and C. We’re given partial pressures of A and B, and we need to find C. By understanding partial pressures, you can apply Dalton's Law to solve for the missing value.

Gas Mixtures

Gas mixtures are common both in nature and various industrial applications. Each gas in a mixture follows its own behavior as if other gases are not present. This independence is key in calculating pressures with Dalton's Law. In our problem, three gases (A, B, and C) form a mixture. Knowing the behavior of gas mixtures aids in applying Dalton’s Law correctly. Here, total pressure results from adding pressures of individual gases. Even without knowing interactions between gases, you can still determine unknown pressures using given data about the other gases.

Total Pressure

Total pressure in a gas mixture is the sum of the partial pressures of all gases present. This is Dalton’s Law in action. In the given exercise, the total pressure of the gas mixture is 6.11 atm. By knowing this, along with the partial pressures of gas A (1.68 atm) and gas B (3.89 atm), you can find the partial pressure of gas C by rearranging the equation: o\[P_{total} = P_A + P_B + P_C\] to solve for \[P_C\]: \[P_C = P_{total} - P_A - P_B\].Substituting, we get \[P_C = 6.11 - 1.68 - 3.89 = 0.54\] atm. This showcases how total pressure helps find individual gas pressures within a mixture.