Problem 48 - Chemistry Matter and Change

Question

In a reaction \(\mathrm{Mg}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{H}_{2}(\mathrm{g})+\mathrm{MgCl}_{2}(\mathrm{aq}),\) 6.00 \(\mathrm{g}\) of Mg was present at 0.00 \(\mathrm{min}\) . After 3.00 \(\mathrm{min}\) , 4.50 gof Mg remained. Express the average rate as mol Mg consumed/min.

Step-by-Step Solution

Answer

The average rate is approximately 0.0207 mol Mg consumed per minute.

Step 1: Determine Initial Moles of Mg

First, calculate the moles of magnesium present initially. The formula to convert grams to moles is:\[\text{moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}}\]The molar mass of Mg is 24.31 g/mol, so:\[\text{moles of Mg}_\text{initial} = \frac{6.00 \text{ g}}{24.31 \text{ g/mol}} \approx 0.247 \text{ mol}\]

Step 2: Determine Remaining Moles of Mg

Next, find the moles of magnesium remaining after 3.00 minutes. Using the same conversion formula, calculate:\[\text{moles of Mg}_\text{remaining} = \frac{4.50 \text{ g}}{24.31 \text{ g/mol}} \approx 0.185 \text{ mol}\]

Step 3: Calculate Moles of Mg Consumed

Determine the moles of Mg consumed by subtracting the remaining moles from the initial moles:\[\text{moles of Mg}_\text{consumed} = 0.247 \text{ mol} - 0.185 \text{ mol} = 0.062 \text{ mol}\]

Step 4: Calculate Average Rate of Reaction

Calculate the rate of the reaction in terms of moles of Mg consumed per minute:\[\text{Rate} = \frac{\text{moles of Mg}_\text{consumed}}{\text{time}} = \frac{0.062 \text{ mol}}{3.00 \text{ min}} \approx 0.0207 \text{ mol/min}\]

Key Concepts

Average Rate of Reaction

The average rate of a chemical reaction offers an insight into how quickly a reactant is consumed or how fast a product is formed over a given time period. In the context of our reaction with magnesium (\( \text{Mg} \)), the average rate specifically tells us how many moles of magnesium are consumed per minute.

To find the average rate, we first calculate the change in moles of magnesium over the time interval. In our example:

• Initial moles of Mg were 0.247 mol, with 0.185 mol remaining after 3 minutes.
• The moles of Mg consumed therefore is 0.062 mol.
• Time elapsed is 3 minutes, so the average rate is \( 0.0207 \text{ mol/min} \).

This indicates that, on average, about 0.0207 moles of magnesium are consumed every minute for the first 3 minutes.

Moles Calculation

Understanding moles is crucial in chemistry as it forms the basis of measuring chemical reactions. The mole is a unit that counts the number of particles, much like a dozen counts 12 items. When converting mass to moles, we use the molar mass, which is the mass of one mole of a substance.

For magnesium, the molar mass is roughly 24.31 g/mol. This means for every 24.31 grams of magnesium, we have one mole.

• To find the moles from a given mass, divide the mass by the molar mass: \( \text{moles} = \frac{\text{mass}}{\text{molar mass}} \)
• Initially, with 6.00 g of Mg, we calculate \( 0.247 \text{ mol} \).
• After 3 minutes, with 4.50 g left, \( 0.185 \text{ mol} \) remains.

This method showcases the straightforwardness of mole calculation, pivotal for understanding more complex chemical reactions and processes.

Magnesium Reaction

The reaction involving magnesium, specifically the interaction of \( \text{Mg} \) and hydrochloric acid (\( \text{HCl} \)), is an excellent example of a single displacement reaction. Here, magnesium displaces hydrogen in the acid, releasing \( \text{H}_2 \) gas and producing magnesium chloride (\( \text{MgCl}_2 \)).

This reaction is very useful in demonstrating basic principles of chemical kinetics and stoichiometry:

• Magnesium starts in solid form and reacts with a liquid (aqueous) hydrochloric acid.
• As the reaction progresses, hydrogen gas and magnesium chloride in solution are produced.
• Observing the time it takes for magnesium to react gives insights into the rate of the reaction.

Such reactions are commonly used in laboratory settings to study reaction rates and to produce hydrogen gas.

Chemical Kinetics

Chemical kinetics explores the speed or rate of chemical reactions and what factors might affect this rate. This is crucial for understanding how quickly reactions reach completion and which conditions can optimize this speed.

In the example of the magnesium and hydrochloric acid reaction:

• The rate of reaction is measured in moles of magnesium consumed per minute, derived from how much magnesium you start with and what remains after a certain time.
• Factors influencing reaction rate could include concentration of \( \text{HCl} \), temperature, and surface area of magnesium.
• A greater concentration or higher temperature typically increases the reaction's rate.

Studying these factors gives a deeper understanding of how to control reactions in experimental and industrial settings, aiding in both the theory and application of chemistry.