Problem 87 - Chemistry Matter and Change

Question

Use the reaction shown below to answer these questions. $$2 \mathrm{CO}(\mathrm{g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{CO}_{2}(\mathrm{g})$$ a. What is the volume ratio of carbon monoxide to carbon dioxide in the balanced equation? b. If 42.7 g of CO is reacted completely at STP, what volume of \(\mathrm{N}_{2}\) gas will be produced?

Step-by-Step Solution

Answer

Volume ratio of CO to CO₂ is 1:1. Volume of \(\text{N}_2\) produced is 17.07 L.

Step 1: Identify Molar Ratios

From the balanced equation \(2 \text{CO}(\text{g}) + 2 \text{NO}(\text{g}) \rightarrow \text{N}_2(\text{g}) + 2 \text{CO}_2(\text{g})\), the molar ratio of CO to CO₂ is 2:2. This simplifies to 1:1, indicating that for every volume of carbon monoxide, the same volume of carbon dioxide is produced.

Step 2: Calculate Moles of CO

Find the molar mass of CO, which is 28.01 g/mol. Use this to convert grams to moles: \[\text{moles of CO} = \frac{42.7 \text{ g CO}}{28.01 \text{ g/mol}} \approx 1.525 \text{ moles CO}\].

Step 3: Determine Moles of \(\text{N}_2\)

The balanced equation shows a 2:1 molar ratio between CO and \(\text{N}_2\). Therefore, use the moles of CO to find moles of \(\text{N}_2\): \[\text{moles of } \text{N}_2 = \frac{1.525 \text{ moles CO}}{2} \approx 0.7625 \text{ moles } \text{N}_2\].

Step 4: Calculate Volume at STP

At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 L. Thus, the volume of \(\text{N}_2\) produced is: \[\text{Volume of } \text{N}_2 = 0.7625 \text{ moles } \times 22.4 \text{ L/mol} \approx 17.07 \text{ L}\].

Key Concepts

Balanced Chemical Equation

A balanced chemical equation is crucial for understanding chemical reactions. It provides a snapshot of the reactants and products involved in a reaction. Each element's atoms are accounted for on both sides of the equation, ensuring the law of conservation of mass is adhered to. This means that matter is neither created nor destroyed in the course of a chemical reaction.
In the equation given, \(2 \text{CO}(\text{g}) + 2 \text{NO}(\text{g}) \rightarrow \text{N}_2(\text{g}) + 2 \text{CO}_2(\text{g})\), the coefficients tell us that:

• 2 molecules of carbon monoxide (CO) react with
• 2 molecules of nitric oxide (NO), producing
• 1 molecule of nitrogen gas (\(\text{N}_2\)) and
• 2 molecules of carbon dioxide (\(\text{CO}_2\)).

Making sure your chemical equation is balanced is essential because it dictates the proportions in which chemicals will react and the quantities of products formed.

Molar Ratio

Molar ratio is a crucial concept for solving stoichiometry problems. It stems from the coefficients of a balanced chemical equation and helps to establish the relationships between the amounts of reactants and products.

• In our equation, the molar ratio of CO to \(\text{CO}_2\) is 2:2, which simplifies to 1:1.
• The molar ratio of CO to \(\text{N}_2\) is 2:1.

This means:

• For every mole (or volume) of carbon monoxide reacted, an equal amount of carbon dioxide is produced.
• For every 2 moles of carbon monoxide, 1 mole of nitrogen gas is produced.

Understanding molar ratios allows you to predict how much of each product you'll get from given amounts of reactants when you quantify them in moles.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP) is a set of conditions that simplifies measurements of gases. STP assumes a temperature of 0°C (273.15 K) and a pressure of 1 atm (101.3 kPa). At STP, it is convenient to use these conditions to perform calculations involving gases because:

• 1 mole of any ideal gas occupies a volume of 22.4 liters.
• This uniform standard makes it easier to compare different gases and predict volumes based on moles.

In our calculation, using the moles of nitrogen gas \((\text{N}_2)\) determined, you can thrive in finding the usable volume at STP using the 22.4 L/mol conversion factor.

Mole-to-Volume Conversion

The mole-to-volume conversion is an essential tool when working with gases at STP. This conversion allows you to take the amount of substance in moles and determine its corresponding volume in liters. For example,

• 1 mole of any gas occupies 22.4 liters at STP.

In our step-by-step solution, after determining that the reaction produced about 0.7625 moles of \(\text{N}_2\), we utilize this conversion to find that it occupies approximately 17.07 liters.

• This calculation is done by multiplying the moles of nitogen available by the volume occupied per mole at STP, using the relation: \(\text{Volume} = \text{moles} \times 22.4\text{ L/mol}\)

This enables you to relate your calculations directly to observable physical quantities, which is often necessary for practical laboratory conditions.