Question

Given the following amounts of gases, calculate the number of moles of each gas. Calculate the volume each amount of gas would occupy at STP. (a) \(5.8 \mathrm{~g} \mathrm{NH}_{3}\) (b) \(48 \mathrm{~g} \mathrm{O}_{2}\) (c) \(10.8 \mathrm{~g}\) He

Short answer

The number of moles of NH3, O2, and He are approximately 0.341 mol, 1.5 mol, and 2.7 mol respectively. The volumes these gases would occupy at STP are approximately 7.63 L, 33.6 L, and 60.48 L respectively.

Step-by-step solution

Calculate the number of moles

The number of moles (\(n\)) can be found by dividing the mass of the gas by its molar mass. For (a) NH3, (b) O2, and (c) He, their molar masses are approximately 17 g/mol, 32 g/mol, and 4 g/mol respectively. Therefore, \(n = \frac{Mass}{Molar~mass}\). For NH3: \(n = \frac{5.8~g}{17~g/mol} \approx 0.341~mol\), for O2: \(n = \frac{48~g}{32~g/mol} = 1.5~mol\), and for He: \(n = \frac{10.8~g}{4~g/mol} = 2.7~mol\).

Calculate the volume at STP

The volume that these gases occupy at STP can be found using Avogadro's principle, which states that equal volumes of gases at the same temperature and pressure contain the same number of molecules. Therefore, at STP, 1 mole of any gas occupies 22.4 L. So, the volume \(V\) of each gas can be found as \(V = n \times 22.4 L/mol\). For NH3: \(V = 0.341~mol \times 22.4 L/mol \approx 7.63 L\), for O2: \(V = 1.5~mol \times 22.4 L/mol = 33.6 L\), and for He: \(V = 2.7~mol \times 22.4 L/mol = 60.48 L\).

Key concepts

Molar Mass

Molar mass is a crucial concept in chemistry, as it helps us find out how heavy one mole of a substance is. This is particularly important when dealing with gases.
To calculate the molar mass, you need to know the atomic mass of each element in the compound. The atomic masses are found on the periodic table. Then, you sum up these values based on the number of each type of atom in the molecule.

• Example: For ammonia (\(\mathrm{NH}_3\)), the molar mass is calculated as follows:
• Nitrogen (N) has an atomic mass of about 14 g/mol.
• Hydrogen (H) has an atomic mass of about 1 g/mol. Since ammonia has three hydrogen atoms, this sums up to 3 g/mol for H.
• Thus, the molar mass of NH3 is 14 + 3 = 17 g/mol.

Understanding molar mass helps when measuring the mass needed to achieve a certain number of moles, crucial for many chemical reactions and gas calculations.

Mole Calculation

Moles are essential in chemistry, as they provide a link between the mass of a substance and the number of atoms or molecules it contains. Calculating moles helps us understand and predict how substances will react.
The basic formula to calculate the number of moles is: \[ n = \frac{\text{Mass of the substance (g)}}{\text{Molar mass (g/mol)}} \] This equation allows you to convert grams into moles.

• For example: if you wish to find the moles of 5.8 g of NH3, use the following:\[ n = \frac{5.8\,g}{17\,g/mol} \approx 0.341\,mol \]
• This means there are about 0.341 moles of ammonia in 5.8 grams.

Similarly, detailed calculations can be performed for other substances once you know their molar mass.

Standard Temperature and Pressure (STP)

STP stands for Standard Temperature and Pressure, a set condition in chemistry used for easy comparison of gases. At STP, the conditions are defined as a temperature of 0°C (273.15 K) and a pressure of 1 atmosphere (atm). These specific conditions were chosen to standardize measurements when comparing different gases.
One important concept related to gases at STP is Avogadro's law. This law states that one mole of any gas occupies the same volume, 22.4 liters, at STP.

• Volume Calculation: To find the volume of a gas at STP, use the formula: \[ V = n \times 22.4\,L/mol \]where \(V\) is the volume and \(n\) is the number of moles of the gas.
• Example: For helium, with 2.7 moles: \[ V = 2.7\,mol \times 22.4\,L/mol = 60.48\,L \]

Using STP conditions simplifies calculations and helps to understand the behavior of gases under standard conditions.