Problem 96 - Introductory Chemistry Atoms First

Question

(a) How many liters of \(\mathrm{O}_{2}\) are there in \(5.38\) moles at STP? (b) How many moles of \(\mathrm{NH}_{3}\) are there in \(859 \mathrm{~mL}\) at STP? (c) How many moles of \(\mathrm{H}_{2}\) are there in \(0.518 \mathrm{~L}\) at STP?

Step-by-Step Solution

Answer

(a) The volume of $\mathrm{O}_{2}$ is \(5.38 \times 22.4 \mathrm{~L}\). (b) The number of moles of $\mathrm{NH}_{3}$ is \( \frac{0.859\mathrm{~L}}{22.4\mathrm{~L/mole}}\). (c) The number of moles of $\mathrm{H}_{2}$ is \( \frac{0.518\mathrm{~L}}{22.4\mathrm{~L/mole}}\).

Step 1: Problem (a)

We are given 5.38 moles of O2 and we need to find its volume at STP. To do so, we'll apply the formula: Volume (L) = Moles × Molar volume at STP So, Volume (L) = 5.38 moles × 22.4 L/mole = \(5.38 × 22.4 \mathrm~L\)

Step 2: Problem (b)

We are given 859 mL of NH3 and need to find its amount in moles at STP. First, convert these 859 mL to liters: 859 mL × (\(1\mathrm{~L} \over 1000\mathrm{~mL}\)) = 0.859 L Now, we can find the number of moles using the formula: Moles = Volume (L) ÷ Molar volume at STP So, Moles = \( \frac{0.859\mathrm{~L}}{22.4\mathrm{~L/mole}}\)

Step 3: Problem (c)

We are given 0.518 L of H2 and need to find its amount in moles at STP. We'll apply the same formula as in problem (b): Moles = Volume (L) ÷ Molar volume at STP So, Moles = \( \frac{0.518\mathrm{~L}}{22.4\mathrm{~L/mole}}\)

Key Concepts

Molar Volume

The concept of molar volume is crucial in chemistry as it simplifies calculations involving gases. Molar volume is the volume one mole of a substance occupies at a given temperature and pressure. At Standard Temperature and Pressure (STP), which is 0°C and 1 atmosphere pressure, the molar volume of an ideal gas is typically accepted as 22.4 liters per mole. This value is rooted in the Ideal Gas Law and provides a convenient way to convert between moles and volume when dealing with gases under standard conditions.

Conversion of Volume to Moles

Converting from volume to moles involves using the molar volume of a gas. This is especially straightforward at STP due to the consistent use of 22.4 liters per mole as a conversion factor. If you have a known volume of a gas, you can determine the number of moles by dividing the volume in liters by 22.4. For example, if you have 0.859 liters of a gas, you would perform the calculation of \[\text{Moles} = \frac{0.859 \text{ L}}{22.4 \text{ L/mole}}\].This formula lets you find out how many moles of gas you are dealing with simply and directly.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed in the formula:\[PV = nRT\],where \(P\) is the pressure, \(V\) is the volume, \(n\) is the number of moles, \(R\) is the universal gas constant, and \(T\) is the temperature in Kelvin. This law is ideal for theoretical predictions and works best for gases under normal conditions, although actual gases may deviate slightly at high pressures or low temperatures. The concept helps understand how changes in one variable affect the others, a crucial aspect when dealing with gases.

Mole Concept

The mole is a base unit in chemistry used to quantify the amount of substance. It is a bridge between the atomic scale and macroscale, allowing chemists to perform large-scale calculations. One mole contains exactly 6.022 x 10\(^{23}\) particles, known as Avogadro's number. This concept allows for translation between individual particles like molecules or atoms and bulk amounts of substance that can be handled physically. Understanding how to work with moles, using tools like molar volume at STP, empowers chemists to predict and calculate the outcomes of reactions and processes.