Question

Suppose one magnesium hydroxide tablet costs 0.0500 dollars. Let each 1.00 g magnesium hydroxide tablet be 100. percent magnesium hydroxide. Using only these tablets, you are required to neutralize 2.00 L of 0.500 M HCl. How much does this cost? Express your answer in dollars.

Answer 1

Answer:

1.46 $.

Explanation:

• Mg(OH)₂ neutralizes HCl according to the balanced reaction:

2HCl + Mg(OH)₂ → MgCl₂ + 2H₂O.

Every 2 moles of HCl are neutralized by 1 mole of Mg(OH)₂.

• At neutralization: The no. of moles of HCl is equal to the no. of moles of Mg(OH)₂.

The no. of moles of HCl = (MV) of HCl = (2.0 L)(0.5 mol/L) = 1.0 mol.

This requires 0.5 mol of Mg(OH)₂ to be neutralized.

∵ no. of moles of Mg(OH)₂ = mass/molar mass.

∴ mass of Mg(OH)₂ = (no. of moles of Mg(OH)₂)(molar mass) = (0.5 mol)(58.32 g/mol) = 29.16 g.

• To find the cost, we can use cross multiplication:

1.0 g of Mg(OH)₂ costs → 0.05 $.

29.16 g of Mg(OH)₂ costs → ??? $.

∴ The cost of tablets = (29.16 g)(0.05 $) = 1.46 $.