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Chapter 5: Problem 83

An unknown diatomic gas has a density of 3.164 g/L at STP. What is the identity of the gas?

Short Answer

Expert verified
The unknown diatomic gas can be identified by calculating its molar mass using the given density at STP. The molar mass is calculated using the formula: \(Molar\; mass = Density \times Molar\; volume\) which comes out to be \(70.88 g/mol\). Comparing this value to the molar masses of known diatomic gases, the unknown diatomic gas is Chlorine (Cl2), having a molar mass of \(70.9 g/mol\).

Step by step solution

01

Write down the given information

We are given the following information: - Density of the unknown gas: \(3.164 \frac{g}{L}\) - Conditions: STP, which means a temperature of \(273.15 K\) and a pressure of \(1 atm\).
02

Understand the relationship between density, molar mass, and molar volume

At STP, one mole of any ideal gas occupies a volume of \(22.4 L\). This is known as the molar volume of an ideal gas at STP. The density of a gas is defined as its mass per unit volume, so we can find its molar mass by using the following equation: \[Density = \frac{molar\; mass}{molar\; volume}\]
03

Calculate the molar mass of the gas

Rearrange the equation in step 2 and solve for the molar mass: \[Molar\; mass = Density \times Molar\; volume\] \[Molar\; mass = 3.164 \frac{g}{L} \times 22.4 L\] \[Molar\; mass = 70.88 g/mol\] The calculated molar mass of the unknown gas is approximately \(70.88 g/mol\).
04

Identify the diatomic gas

Now compare the calculated molar mass with the molar mass of known diatomic gases: - Hydrogen (H2): \(2 g/mol\) - Nitrogen (N2): \(28 g/mol\) - Oxygen (O2): \(32 g/mol\) - Fluorine (F2): \(38 g/mol\) - Chlorine (Cl2): \(70.9 g/mol\) - Bromine (Br2): \(160 g/mol\) - Iodine (I2): \(254 g/mol\) Our calculated molar mass (\(70.88 g/mol\)) is closest to the molar mass of Chlorine (Cl2), which is \(70.9 g/mol\). Therefore, we can conclude that the unknown diatomic gas is Chlorine (Cl2).

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