To determine the mass of magnesium (Mg) required to react with 250 cm³ of 0.5 M hydrochloric acid (HCl), we will follow a systematic approach. Let's break down the problem step-by-step. ### Step 1: Understand the Reaction The balanced chemical equation is: \[ \text{Mg(s)} + 2\text{HCl(aq)} \rightarrow \text{MgCl}_2\text{(aq)} + \text{H}_2\text{(g)} \] From this equation, we can see that: - 1 mole of magnesium reacts with 2 moles of hydrochloric acid. ### Step 2: Calculate the Moles of HCl We need to find out how many moles of HCl are present in 250 cm³ of a 0.5 M solution. 1. **Convert cm³ to L**: \[ 250 \text{ cm}^3 = 250 \div 1000 = 0.250 \text{ L} \] 2. **Use the molarity formula**: \[ \text{Moles of HCl} = \text{Molarity} \times \text{Volume in L} \] \[ \text{Moles of HCl} = 0.5 \, \text{mol/L} \times 0.250 \, \text{L} = 0.125 \, \text{mol} \] ### Step 3: Determine the Moles of Mg Required From the balanced equation, we know that 2 moles of HCl react with 1 mole of Mg. Therefore, we can set up a ratio to find the moles of Mg needed for 0.125 moles of HCl. \[ \text{Moles of Mg} = \frac{1 \, \text{mol Mg}}{2 \, \text{mol HCl}} \times 0.125 \, \text{mol HCl} = \frac{0.125}{2} = 0.0625 \, \text{mol Mg} \] ### Step 4: Calculate the Mass of Mg Now that we have the moles of magnesium, we can calculate the mass using the molar mass of magnesium. 1. **Use the formula for mass**: \[ \text{Mass} = \text{Moles} \times \text{Molar Mass} \] \[ \text{Mass of Mg} = 0.0625 \, \text{mol} \times 24 \, \text{g/mol} = 1.5 \, \text{g} \] ### Conclusion The mass of magnesium required to react with 250 cm³ of 0.5 M HCl is **1.5 g**. Therefore, the correct option is **B**. ### Explanation of Other Options - **Option A (0.3 g)**: This is too low. It suggests that only a fraction of the required magnesium is being considered, which does not align with the stoichiometry of the reaction. - **Option C (2.4 g)**: This is too high. It implies that more magnesium is needed than what is calculated based on the moles of HCl available. - **Option D (3.0 g)**: This is also too high and reflects a misunderstanding of the stoichiometric relationship between magnesium and hydrochloric acid. ### Revision Summary - The balanced equation shows the stoichiometric relationship between Mg and HCl. - Calculate moles of HCl using molarity and volume. - Use stoichiometry to find moles of Mg required. - Convert moles of Mg to mass using its molar mass. This systematic approach ensures that you can tackle similar problems effectively in the future!