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Chapter 9: Problem 1323

For a gas \(\left(R / C_{V}\right)=0.67\). This gas is made up of molecules which are (A) Diatomic (B) monoatomic (C) polyatomic (D) mixture of diatomic and polyatomic molecules

Short Answer

Expert verified
The given ratio of \(R / C_{V} = 0.67\) does not match the expected ratios for monoatomic (\(R/C_{V} = 3\)), diatomic (\(R/C_{V} = 1.67\)), or polyatomic (\(R/C_{V} = 1.4\)) gases. Therefore, the gas is likely a mixture of different types of molecules, specifically a mixture of diatomic and polyatomic molecules. The correct answer is (D) mixture of diatomic and polyatomic molecules.

Step by step solution

01

Recall the Ratios for Different Types of Molecules

For monoatomic, diatomic, and polyatomic molecules, the ratios of \(R/C_{V}\) are as follows: 1. Monoatomic: \(R/C_{V} = \frac{3}{3 - 2} = \frac{3}{1} = 3\) 2. Diatomic: \(R/C_{V} = \frac{5}{5 - 2} = \frac{5}{3} = 1.67\) 3. Polyatomic: \(R/C_{V} = \frac{7}{7 - 2} = \frac{7}{5} = 1.4\) Now we will compare the given ratio to these values.
02

Compare the Given Ratio to Expected Ratios

The given ratio is \(R / C_{V} = 0.67\). Now we will compare this value to the expected ratios for each type of molecule in order to identify the type of molecules present in the gas: 1. Monoatomic (\(R/C_{V}\) = 3): The given ratio is not equal to the expected ratio for a monoatomic gas. 2. Diatomic (\(R/C_{V}\) = 1.67): The given ratio is not equal to the expected ratio for a diatomic gas. 3. Polyatomic (\(R/C_{V}\) = 1.4): The given ratio is not equal to the expected ratio for a polyatomic gas. Since the given ratio doesn't match the expected ratio for any single type of molecule (monoatomic, diatomic, or polyatomic), we can conclude that the gas is likely a mixture of different types of molecules.
03

Select the Correct Option

Given the comparison of the given ratio to the expected ratios for each type of molecule, we conclude that the gas is made up of molecules that are a mixture of diatomic and polyatomic molecules. So, the correct option is: (D) mixture of diatomic and polyatomic molecules

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