Problem 31 - Chemistry The Central Science In Si Units

Question

Suppose you are given two 2 -L flasks and told that one contains a gas of molar mass 28 , the other a gas of molar mass 56 , both at the same temperature and pressure. The mass of gas in the flask \(A\) is \(1.0 \mathrm{~g}\) and the mass of gas in the flask \(\mathrm{B}\) is \(2.0 \mathrm{~g}\). Which flask contains the gas of molar mass \(28,\) and which contains the gas of molar mass \(56 ?\)

Step-by-Step Solution

Answer

Flask A contains the gas with molar mass 28, and flask B contains the gas with molar mass 56.

Step 1: Understanding Molar Mass and Mass Given

You are given two gases in different flasks with molar masses 28 and 56, and masses of 1.0 g in flask A and 2.0 g in flask B. Both gases are at the same temperature and pressure.

Step 2: Use the Ideal Gas Law

Since the temperature and pressure of both gases are the same, we can compare moles using the ideal gas law, focusing on the relationships between mass, molar mass, and number of moles: \[ n = \frac{m}{M} \] where \(n\) is the number of moles, \(m\) is the mass, and \(M\) is the molar mass.

Step 3: Calculate Moles of Gas in Flask A

For flask A with mass 1.0 g, calculate the moles for each potential molar mass case: 1. For molar mass 28: \[ n_{A,28} = \frac{1.0}{28} = 0.0357 \]2. For molar mass 56: \[ n_{A,56} = \frac{1.0}{56} = 0.0179 \]

Step 4: Calculate Moles of Gas in Flask B

For flask B with mass 2.0 g, calculate the moles for each potential molar mass case: 1. For molar mass 28: \[ n_{B,28} = \frac{2.0}{28} = 0.0714 \]2. For molar mass 56: \[ n_{B,56} = \frac{2.0}{56} = 0.0357 \]

Step 5: Compare Moles and Determine Which Flask Contains Which Gas

The number of moles should be similar for both flasks since they are under the same conditions of temperature and pressure. Comparing the calculated moles: - Using molar mass 28 for flask B gives more moles (0.0714) than either case for flask A. - Using molar mass 56 for flask B gives moles (0.0357) equal to flask A if it uses molar mass 28 (0.0357). Therefore, flask A contains the gas with molar mass 28 (as their moles match), and flask B contains the gas with molar mass 56.

Key Concepts

Molar Mass

Molar mass is a vital concept in chemistry, especially when dealing with gases. It refers to the mass of one mole of a substance, expressed in grams per mole (g/mol). Understanding molar mass helps in identifying substances, here particularly when comparing gases.
The molar mass links the mass of a sample to the number of moles it contains 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.
In the context of the original exercise, we are given the masses of gas samples in two flasks and their potential molar masses. By using this fundamental equation, we can calculate the number of moles for each case and thus determine which gas matches each molar mass. This helps us to infer the identity of the gases in the flasks.

Chemical Flasks

Chemical flasks are laboratory tools used for containing, storing, and sometimes reacting substances. In gas-related experiments, flasks can be crucial for understanding the conditions under which gas samples are kept.
In the given exercise, we use flasks to contain gases of known molar masses at specified conditions. Both flasks are the same size (2 liters), indicating that any change in measured properties comes from differences in the gases themselves, and not from variations in container size or atmospheric conditions.
It's essential to know that these conditions include consistent temperature and pressure across both flasks. This consistency allows us to directly compare the amount of gas, in moles, contained within each flask using the ideal gas law equation. By ensuring all external conditions are equal, the properties of the gases themselves dictate which one matches our expectations for each molar mass.

Gas Properties

The properties of gases, such as their volume, temperature, pressure, and amount, are key to understanding gas behavior. The Ideal Gas Law is a critical component when analyzing these properties.
The ideal gas law equation is represented as:

• \[ PV = nRT \]

Where \( P \) is pressure, \( V \) is volume, \( n \) is the number of moles, \( R \) is the ideal gas constant, and \( T \) is temperature in Kelvin. This law is often used to relate these variables to predict how a gas will behave under different conditions. In our exercise, since both gases are in 2-liter flasks under the same temperature and pressure, we only need to focus on the number of moles (\( n \)). Using the formula \( n = \frac{m}{M} \), we can determine which gas corresponds to which molar mass. By analyzing gas properties, we conclude that flask A must contain the gas with molar mass 28, while flask B holds the gas with molar mass 56, as this matches the comparisons of moles derived from their given masses and potential molar masses.