Problem 40 - Chemistry

Question

Calculate its volume (in liters) of \(88.4 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) at STP.

Step-by-Step Solution

Answer

The volume of 88.4 g of \(\mathrm{CO}_{2}\) at STP is 44.8 L.

Step 1: Determining the molar mass

First, we need to determine the molar mass of carbon dioxide (\( \mathrm{CO}_{2}\)), in terms of grams per mole (\( g/mol \)). Carbon has a molar mass of 12.01 g/mol and oxygen has a molar mass of 16.00 g/mol. Since there are two oxygen atoms for every one carbon atom in \( \mathrm{CO}_{2}\), the molar mass \( M \) is \( 12.01 g/mol + 2 * 16.00 g/mol = 44.01 g/mol \).

Step 2: Calculating number of moles

Next, divide the mass given in the problem by the molar mass of \( \mathrm{CO}_{2}\) to find the number of moles \( n \). We know the mass \( m \) is 88.4 g and the molar mass \( M \) is 44.01 g/mol, so the number of moles \( n \) is \( m / M = 88.4 \, g / 44.01 \, g/mol = 2 \, moles \).

Step 3: Calculating volume

Finally, multiply the number of moles of \( \mathrm{CO}_{2}\) by the volume that one mole of any gas occupies at STP. We know that one mole of any gas occupies a volume of 22.4 liters at STP. So, the volume \( V \) is \( n * 22.4 \, L/mol = 2 \, moles * 22.4 \, L/mol = 44.8 \, L \). So, 88.4 g of \( \mathrm{CO}_{2}\) at STP occupies a volume of 44.8 liters.

Key Concepts

Molar Mass

Understanding molar mass is essential when dealing with gas laws. The molar mass of a compound is the mass of one mole of that substance, typically expressed in grams per mole (g/mol). For carbon dioxide (\(\mathrm{CO}_2\)), the molar mass is calculated by adding the atomic masses of its constituent elements. Carbon has a molar mass of 12.01 g/mol and oxygen is 16.00 g/mol. Since there are two oxygen atoms, you calculate \(12.01 + 2 \times 16.00 = 44.01 \ g/mol\) for \(\mathrm{CO}_2\). Knowing the molar mass helps in converting between the mass of a substance and the number of moles.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure, or STP, is a set of conditions used as a reference point in gas calculations. At STP, the temperature is 0°C (273.15 K) and the pressure is 1 atmosphere (atm). This standardization aids in comparing different gas samples and simplifies calculations. At STP, one mole of any ideal gas occupies 22.4 liters. This concept is crucial for converting between moles and volume in gas law problems.

Mole Calculation

Moles are a fundamental unit in chemistry representing a specific amount of substance. To determine the number of moles from a given mass, divide the mass by the molar mass of the compound. In this exercise, the mass of \(\mathrm{CO}_2\) is 88.4 g. By using the molar mass \(44.01 \ g/mol\), the calculation is \(88.4 \ g \/ 44.01 \ g/mol = 2\ moles\). Understanding mole conversions ensures accurate calculations for reactions and gas volumes.

Volume of Gas at STP

The volume of a gas at STP is determined using the relationship where one mole of gas occupies 22.4 liters. For the problem at hand, after calculating that there are 2 moles of \(\mathrm{CO}_2\), you multiply the moles by the volume per mole at STP: \(2 \times 22.4 \ L/mol = 44.8 \ L\). This demonstrates how moles can be directly translated into a volume measurement using standard conditions.