Consider reacting 100.0mg magnesium with 20.0mL of 1.0M hydrochloric acid. Which reactant is the limiting reagent? What is the theoretical yield of hydrogen? Express answers in millimoles.

Can you please describe the steps taken in order to find the answer as well? Thank you.

To determine the limiting reagent and theoretical yield of hydrogen in this reaction, we need to follow a few steps:

Step 1: Convert grams to moles for each reactant.

Given:
Mass of magnesium (Mg) = 100.0 mg
Volume of hydrochloric acid (HCl) = 20.0 mL
Concentration of HCl = 1.0 M

First, we convert the mass of magnesium to moles:
1. Calculate the molar mass of magnesium (Mg):
Molar mass of Mg = 24.31 g/mol

2. Convert the mass of Mg to moles:
Moles of Mg = (Mass of Mg) / (Molar mass of Mg)
Moles of Mg = 100.0 mg / 24.31 g/mol
Moles of Mg = 4.11 mmol

Next, for the hydrochloric acid (HCl):
1. Convert the volume of HCl to liters:
Volume of HCl = 20.0 mL = 20.0 mL / 1000 mL/L = 0.020 L

2. Calculate the moles of HCl using the concentration:
Moles of HCl = (Volume of HCl) x (Concentration of HCl)
Moles of HCl = 0.020 L x 1.0 mol/L
Moles of HCl = 0.020 mol

Step 2: Determine the stoichiometry of the balanced chemical equation.

The balanced chemical equation for the reaction between magnesium and hydrochloric acid is:

Mg + 2HCl -> MgCl2 + H2

From the balanced equation, we see that 1 mole of Mg reacts with 2 moles of HCl to produce 1 mole of H2.

Step 3: Compare the moles of each reactant to determine the limiting reagent.

We need to compare the moles of Mg with the moles of HCl to identify the limiting reagent. The limiting reagent is the reactant that is completely consumed in the reaction and determines the maximum amount of product that can be formed.

In this case, we see that 4.11 mmol of Mg is greater than 0.020 mmol of HCl. This indicates that Mg is present in excess, and HCl is the limiting reagent.

Step 4: Calculate the theoretical yield of hydrogen.

Since HCl is the limiting reagent, we can use its moles to determine the theoretical yield of hydrogen.

From the balanced equation, we know that 2 moles of HCl can produce 1 mole of H2. Therefore, the theoretical yield of hydrogen is equal to half the number of moles of HCl.

Theoretical yield of H2 = (0.020 mol HCl) * (1 mol H2 / 2 mol HCl)
Theoretical yield of H2 = 0.010 mol

Step 5: Conversion to millimoles.

To express the answers in millimoles, we convert the moles to millimoles by multiplying by 1000.

Theoretical yield of H2 = 0.010 mol * 1000 mmol/mol
Theoretical yield of H2 = 10 mmol

Therefore, the limiting reagent is hydrochloric acid, and the theoretical yield of hydrogen is 10 millimoles.