Problem 100 - Chemistry and Chemical Reactivity

Question

If equal masses of \(\mathrm{O}_{2}\) and \(\mathrm{N}_{2}\) are placed in separate containers of equal volume at the same temperature, which of the following statements is true? If false, explain why it is false. (a) The pressure in the flask containing \(\mathrm{N}_{2}\) is greater than that in the flask containing \(\mathbf{O}_{2}\) (b) There are more molecules in the flask containing \(\mathrm{O}_{2}\) than in the flask containing \(\mathrm{N}_{2}\)

Step-by-Step Solution

Answer

(a) True - higher pressure in \(\text{N}_2\). (b) False - more molecules in \(\text{N}_2\).

Step 1: Understanding the Problem Statement

We have two separate containers of equal volume at the same temperature, each containing an equal mass of either \(\text{O}_2\) or \(\text{N}_2\). We need to evaluate statements (a) and (b) about the pressures and the number of molecules in these containers.

Step 2: Analyzing Statement (a)

Statement (a) claims that the pressure in the flask containing \(\text{N}_2\) is greater than that in the flask with \(\text{O}_2\). According to the ideal gas law, \( PV = nRT \), where \(n\) is the number of moles. Since the masses are equal, check which gas has more moles. The molar mass of \(\text{N}_2\) is approximately 28 g/mol, and for \(\text{O}_2\), it is approximately 32 g/mol. Since \(\text{N}_2\) has a lower molar mass, there are more moles of \(\text{N}_2\) for the same mass, leading to higher pressure in the \(\text{N}_2\) flask. Statement (a) is true.

Step 3: Analyzing Statement (b)

Statement (b) claims that there are more molecules in the flask containing \(\text{O}_2\) than in the flask containing \(\text{N}_2\). Since \(\text{N}_2\) has a smaller molar mass than \(\text{O}_2\), it will have more moles (and thus more molecules) in the same mass compared to \(\text{O}_2\). So, this statement is false. There are more molecules in the \(\text{N}_2\) flask.

Key Concepts

Molar Mass

Molar mass refers to the mass of one mole of a substance. This concept is crucial in chemistry as it helps in converting between grams and moles.

• The molar mass of a substance is expressed in grams per mole (g/mol).
• Each element's molar mass can be found on the periodic table as the atomic weight of the element in grams/mole.
• For molecules like \( \text{O}_2 \) and \( \text{N}_2 \), add the atomic masses from the periodic table.

In our scenario, \( \text{O}_2 \) has a molar mass of approximately 32 g/mol, while \( \text{N}_2 \) has a molar mass of approximately 28 g/mol. Given equal masses of these gases, \( \text{N}_2 \) will have more moles because it has a lower molar mass. This means more molecules are present for the same mass, affecting both pressure and the number of moles.

Moles and Molecules

The mole is a unit used in chemistry to express amounts of a chemical substance. One mole is \( 6.022 \times 10^{23} \) entities of the substance, typically atoms or molecules.

• Using the formula \( n = \frac{m}{M} \), where \( n \) is the number of moles, \( m \) is the mass in grams, and \( M \) is the molar mass.
• For a given mass, if a substance has a lower molar mass, it results in more moles.
• More moles indicate more molecules are present.

In the given exercise, since \( \text{N}_2 \) has a smaller molar mass than \( \text{O}_2 \), equal masses of these gases result in more moles of \( \text{N}_2 \) than \( \text{O}_2 \). Thus, the \( \text{N}_2 \) container contains more molecules. Remember, more molecules mean more moles!

Pressure Comparisons

Pressure is an essential concept in chemistry, particularly when dealing with gases. The Ideal Gas Law connects pressure (\( P \)), volume (\( V \)), moles (\( n \)), and temperature (\( T \)) via the equation \( PV = nRT \), where \( R \) is the ideal gas constant.

• For a fixed volume and temperature, pressure is directly proportional to the number of moles of gas.
• Thus, more moles mean higher pressure in the container.
• Given that pressure is higher if there are more gas molecules present, it implies more collisions with the container walls.

In this exercise, because \( \text{N}_2 \) has more moles than \( \text{O}_2 \) due to its lower molar mass, the pressure in the \( \text{N}_2 \) container will be greater than in the \( \text{O}_2 \) container for identical volumes and temperatures. This demonstrates the direct relationship between the number of moles and gas pressure under constant conditions.