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Chapter 11: Problem 9

Suppose you have a sample of \(\mathrm{CO}_{2}\) gas and want to know its mass without bothering to use a balance. How could you do this?

Short Answer

Expert verified
To find the mass of the CO₂ gas sample without using a balance, first identify the pressure, volume, and temperature of the gas. Then, use the ideal gas law equation, \(PV = nRT\), to calculate the number of moles (n). Find the molar mass of CO₂ by adding the molar mass of one carbon atom (12.01 g/mol) and two oxygen atoms (2 x 16.00 g/mol), resulting in a molar mass of 44.01 g/mol. Finally, calculate the mass of the CO₂ gas by multiplying the number of moles (n) by the molar mass of CO₂ (44.01 g/mol): \(m = n \times 44.01 \frac{g}{mol}\).

Step by step solution

01

Identify the properties of the gas

In order to find the number of moles of the CO₂ gas, we need to know its pressure, temperature, and volume. Usually, these values will be given in the problem, and they'll be needed to determine the number of moles.
02

Calculate the number of moles

Once you have the pressure (P), volume (V), and temperature (T) of the CO₂ gas, you can use the ideal gas law to find the number of moles (n). The ideal gas law is given by the equation: \(PV = nRT\) where R is the ideal gas constant (\(8.314 \frac{J}{molK}\)). Rearrange the ideal gas law equation to solve for n: \(n = \frac{PV}{RT}\) Plug in the values for P, V, and T, and calculate the number of moles of CO₂ gas: \(n = \frac{P \cdot V}{R \cdot T}\)
03

Calculate the molar mass of CO₂

The molar mass of CO₂ can be found by adding the molar masses of one carbon atom and two oxygen atoms. Molar mass of carbon: 12.01 g/mol Molar mass of oxygen: 16.00 g/mol Thus, the molar mass of CO₂ is: \(M_{CO₂} = 12.01 \frac{g}{mol} + 2 \times 16.00 \frac{g}{mol} = 44.01 \frac{g}{mol}\)
04

Calculate the mass of the CO₂ gas

Now that we have the number of moles (n) and the molar mass (M) of CO₂, we can calculate the mass (m) of the CO₂ gas using the equation: \(m = n \times M_{CO₂}\) Plug in the values for n and M and calculate the mass of the CO₂ gas: \(m = n \times 44.01 \frac{g}{mol}\) This will give you the mass of the CO₂ gas sample without having to use a balance.

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