Problem 30 - Chemistry and Chemical Reactivity

Question

Acetaldehyde is a common liquid compound that vaporizes readily. Determine the molar mass of acetaldehyde from the following data: Sample mass \(=0.107\) g Volume of gas \(=125 \mathrm{mL}\) Temperature \(=0.0^{\circ} \mathrm{C} \quad\) Pressure \(=331 \mathrm{mm} \mathrm{Hg}\)

Step-by-Step Solution

Answer

The molar mass of acetaldehyde is approximately 43.67 g/mol.

Step 1: Convert Volume to Liters

The volume of the gas is given as 125 mL. We need to convert this to liters because the gas law equations use liters. Recall that 1 L = 1000 mL, so we have \( V = \frac{125 \text{ mL}}{1000} = 0.125 \text{ L} \).

Step 2: Convert Temperature to Kelvin

The temperature given is 0.0°C. To use the ideal gas law, we need to convert this to Kelvin. The conversion formula is \( T(K) = T(°C) + 273.15 \). Thus, \( T = 0.0 + 273.15 = 273.15 \text{ K} \).

Step 3: Convert Pressure to Atmospheres

The pressure is given as 331 mm Hg. We need to convert this to atmospheres since standard gas law calculations use atmospheres. The conversion factor is 1 atm = 760 mm Hg. So, \( P = \frac{331 \text{ mm Hg}}{760 \text{ mm Hg/atm}} \approx 0.4355 \text{ atm} \).

Step 4: Apply the Ideal Gas Law

Use the ideal gas law formula \( PV = nRT \) to determine the number of moles \( n \). Rearrange to solve for \( n \): \( n = \frac{PV}{RT} \). Use \( R = 0.0821 \text{ L atm/mol K} \). Substitute the converted values: \( n = \frac{(0.4355 \text{ atm})(0.125 \text{ L})}{(0.0821 \text{ L atm/mol K})(273.15 \text{ K})} \approx 0.00245 \text{ mol} \).

Step 5: Calculate Molar Mass

Molar mass (M) is calculated by dividing the mass of the sample by the number of moles \( n \). We have mass = 0.107 g and \( n = 0.00245 \text{ mol} \). Thus, \( M = \frac{0.107 \text{ g}}{0.00245 \text{ mol}} \approx 43.67 \text{ g/mol} \).

Key Concepts

Molar Mass Calculation

Molar mass is a crucial concept that helps in identifying the mass of one mole of a substance. It's usually expressed in grams per mole (g/mol). To find the molar mass of a compound like acetaldehyde, you need the mass of the sample and the number of moles present in the sample.
Here's a quick guideline on calculating molar mass:

• First, determine the number of moles using the ideal gas law: \( PV = nRT \).
• Rearrange the equation to solve for moles: \( n = \frac{PV}{RT} \).
• Apply the known values for pressure (P), volume (V), the gas constant (R), and temperature (T) to find \( n \).
• Finally, divide the mass of your sample by the number of moles to calculate the molar mass: \( M = \frac{\text{mass}}{n} \).

Understanding the molar mass helps in predicting how a substance will react chemically and its physical properties.

Gas Volume Conversion

In the realm of gas laws, converting volumes is a common task. Since gas law calculations often require volumes in liters, you'll need to convert from milliliters if the initial information is given in that form.
The conversion is straightforward because 1 liter (L) is equivalent to 1000 milliliters (mL). To convert mL to L, simply divide the number of milliliters by 1000. For example:

• For 125 mL of gas, the conversion to liters is: \( V = \frac{125 \text{ mL}}{1000} = 0.125 \text{ L} \).

Always remember that using consistent units saves you from errors while applying formulas like the ideal gas law.

Temperature Conversion

Temperature in gas law calculations is expressed in Kelvin (K), as it reflects absolute thermal energy. To convert from Celsius to Kelvin, you just add 273.15 to the Celsius temperature. This conversion is non-negotiable for accurate gas law applications.
For example, if your given temperature is 0.0°C:

• Using the conversion formula: \( T(K) = T(°C) + 273.15 \).
• Thus, \( T = 0.0 + 273.15 = 273.15 \text{ K} \).

Switching to Kelvin eliminates the issue of negative numbers in calculations and ensures uniformity across physical science applications.

Pressure Conversion

Pressure conversion is another essential step when working with gas laws, as standard equations typically use pressure in atmospheres (atm). Often, pressure is initially provided in different units, like millimeters of mercury (mm Hg), requiring conversion for consistency.
To convert mm Hg to atm, utilize the conversion factor where 1 atm equals 760 mm Hg. For example, if you have a pressure of 331 mm Hg:

• Convert it to atm using: \( P = \frac{331 \text{ mm Hg}}{760 \text{ mm Hg/atm}} \approx 0.4355 \text{ atm} \).

This conversion ensures proper unit utilization when applying the ideal gas law formula, preventing miscalculations.