To address the given problem, we will consider each part separately. Here are the steps:
A. Calculating moles of magnesium hydroxide to react with 0.321 moles of hydrochloric acid
1. Write the balanced chemical equation:
[tex]\[
Mg(OH)_2 + 2 HCl \rightarrow 2 H_2O + MgCl_2
\][/tex]
2. From the equation, we see that 1 mole of [tex]\( Mg(OH)_2 \)[/tex] reacts with 2 moles of [tex]\( HCl \)[/tex].
3. We are given 0.321 moles of [tex]\( HCl \)[/tex].
4. Calculate the moles of [tex]\( Mg(OH)_2 \)[/tex] required using the stoichiometric relationship:
[tex]\[
\text{Moles of } Mg(OH)_2 = \frac{\text{Moles of } HCl}{2} = \frac{0.321}{2} = 0.1605
\][/tex]
B. Calculating the molar mass of magnesium hydroxide
1. The chemical formula of magnesium hydroxide is [tex]\( Mg(OH)_2 \)[/tex].
2. The atomic masses are:
- [tex]\( Mg \)[/tex]: 24.305 g/mol
- [tex]\( O \)[/tex]: 16.00 g/mol
- [tex]\( H \)[/tex]: 1.008 g/mol
3. Calculate the molar mass of [tex]\( Mg(OH)_2 \)[/tex]:
[tex]\[
\text{Molar mass of } Mg(OH)_2 = 24.305 + 2 \times (16.00 + 1.008) = 24.305 + 2 \times 17.008 = 24.305 + 34.016 = 58.321 \text{ g/mol}
\][/tex]
C. Calculating the molar mass of hydrochloric acid
1. The chemical formula of hydrochloric acid is [tex]\( HCl \)[/tex].
2. The atomic masses are:
- [tex]\( H \)[/tex]: 1.008 g/mol
- [tex]\( Cl \)[/tex]: 35.453 g/mol
3. Calculate the molar mass of [tex]\( HCl \)[/tex]:
[tex]\[
\text{Molar mass of } HCl = 1.008 + 35.453 = 36.461 \text{ g/mol}
\][/tex]
D. Calculating the grams of hydrochloric acid needed to react with 6.50 g of magnesium hydroxide
1. Calculate the moles of [tex]\( Mg(OH)_2 \)[/tex] from its given mass:
[tex]\[
\text{Moles of } Mg(OH)_2 = \frac{\text{Mass of } Mg(OH)_2}{\text{Molar mass of } Mg(OH)_2} = \frac{6.50}{58.321} = 0.1114 \text{ moles}
\][/tex]
2. From the balanced equation, 1 mole of [tex]\( Mg(OH)_2 \)[/tex] reacts with 2 moles of [tex]\( HCl \)[/tex]. Therefore, the moles of [tex]\( HCl \)[/tex] required are:
[tex]\[
\text{Moles of } HCl = 0.1114 \times 2 = 0.223 \text{ moles}
\][/tex]
3. Calculate the mass of [tex]\( HCl \)[/tex] needed:
[tex]\[
\text{Mass of } HCl = \text{Moles of } HCl \times \text{Molar mass of } HCl = 0.223 \times 36.461 = 8.127 \text{ g}
\][/tex]
Hence, the solutions to the respective parts are:
- A. 0.1605 moles of [tex]\( Mg(OH)_2 \)[/tex] are required to react with 0.321 moles of [tex]\( HCl \)[/tex].
- B. The molar mass of [tex]\( Mg(OH)_2 \)[/tex] is 58.321 g/mol.
- C. The molar mass of [tex]\( HCl \)[/tex] is 36.461 g/mol.
- D. To react with 6.50 g of [tex]\( Mg(OH)_2 \)[/tex], you need 8.127 g of [tex]\( HCl \)[/tex].
