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 min, 4.50 \(\mathrm{g}\) of Mg remained. Express the average rate as mol Mg consumed/min.

Short answer

The average rate of the reaction is: Average rate (mol Mg/min) = \(\frac{6.00 \ g - 4.50 \ g}{3.00 \ min \times 24.31 \ \frac{g}{mol}}\) = \(\frac{1.50 \ g}{3.00 \ min \times 24.31 \ \frac{g}{mol}}\) = \(0.0205 \ mol \ Mg/min\)

Step-by-step solution

Convert grams of Mg to moles

To convert grams of magnesium into moles, we use the molar mass of magnesium. The molar mass of Mg is 24.31 g/mol. We can use the following formula: moles = mass (g) / molar mass (g/mol) Initially, moles_initial = 6.00 g / 24.31 g/mol After 3 minutes, moles_remaining = 4.50 g / 24.31 g/mol

Calculate the change in moles

Now that we have the initial and remaining moles of magnesium, we can find the change in moles of Mg by subtracting the remaining moles from the initial moles. moles_change = moles_initial - moles_remaining

Calculate the average rate of reaction in mol Mg/min

Now we can find the average rate of the reaction in mol Mg consumed/min. We know the change in moles of Mg and the time duration of 3 minutes. Therefore, the average rate can be calculated as follows: Average rate (mol Mg/min) = moles_change / time (min) Plug in the values and calculate the result.

Key concepts

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that deals with the quantitative relationships between reactants and products in a chemical reaction. By understanding stoichiometry, students can predict the amounts of substances consumed and produced during chemical reactions.

This crucial concept is fundamentally tied to the Law of Conservation of Mass, which states that mass is neither created nor destroyed in a chemical reaction. Stoichiometric calculations, which are often represented by balanced chemical equations, enable chemists and students alike to calculate the exact amounts of reactants needed to react completely, or the amounts of products formed from a given quantity of reactants.

For instance, in the provided exercise, magnesium reacts with hydrochloric acid to produce hydrogen gas and magnesium chloride. The balanced equation indicates that one mole of magnesium reacts with two moles of hydrochloric acid to produce one mole of hydrogen gas and one mole of magnesium chloride. Hence, stoichiometry helps in finding the mol-to-mol conversion between reactants and products.

Molar Mass Calculation

The molar mass calculation is vital as it bridges the gap between the macroscopic world of laboratory measurements and the microscopic world of atoms and molecules. As defined, the molar mass of an element or compound is the mass in grams of one mole of that substance. One mole, in turn, contains Avogadro's number of particles, which is roughly 6.022 x 10²³ entities.

For example, magnesium has an atomic mass of approximately 24.31 amu (atomic mass units), and this translates directly to a molar mass of 24.31 g/mol when considering one mole of magnesium atoms. In our exercise, we utilize the molar mass of magnesium to convert the mass of Mg in grams to the amount in moles, an essential step to calculating stoichiometric ratios and subsequently the rate of a chemical reaction.

Chemical Kinetics

Chemical kinetics is the branch of chemistry that concerns the rates at which reactions occur and the steps by which they proceed. Knowing the rate of a reaction is important in both industrial and laboratory settings, as it determines how long a reaction takes and how it can be controlled.

When talking about chemical kinetics, the term 'rate' refers to the speed of the reaction, or how fast the reactants are converted into products. This can be expressed in terms of the rate of disappearance of reactants or the rate of appearance of products. In the exercise, we are interested in calculating the average rate at which magnesium is consumed, which is found by measuring the decrease in magnesium over the 3-minute period. The average rate of reaction then informs us about the speed of the reaction under specific conditions, which is a practical insight for chemists planning or analyzing the course of chemical processes.