Question

What mass of your hydrate would be required to create 1.00 cup of water? Use dimensional analysis to solve this problem.

BaCl₂ is your hydrate
- 0.96g BaCl₂
- 0.17g H₂O
- 0.0046 moles BaCl₂
- 0.0094 moles H₂O
- 2 moles H₂O/1 mole BaCl₂

Answer 1

To create 1.00 cup of water from BaCl₂ hydrate would require approximately 1387 grams of the hydrate, calculated using dimensional analysis based on the mole ratio and molar mass of BaCl₂ and H₂O.

Step-by-step explanation:

The question asks how much of BaCl₂ hydrate is needed to produce 1.00 cup of water using dimensional analysis. Given the information that 0.0046 moles of BaCl₂ yield 0.0094 moles of H₂O, and the mole ratio is 2 moles of H₂O per 1 mole of BaCl₂, we can find out the mass of BaCl₂ needed.

To begin, we know that 1 cup of water weighs approximately 240 grams since the density of water is about 1 g/mL and 1 cup is about 240 mL. Using Example 5.3.4, we convert this mass of water to moles, knowing that the molar mass of water is 18.02 g/mol:

1. 240 g H₂O × (1 mol H₂O / 18.02 g H₂O) = 13.32 moles H₂O

This is the amount of water we need to create from the hydrate. Now we use the provided mole ratio of H₂O to BaCl₂:

1. 13.32 moles H₂O × (1 mole BaCl₂ / 2 moles H₂O) = 6.66 moles BaCl₂

Finally, we use the molar mass of BaCl₂, which is not provided but can be calculated based on the periodic table values (137.33 g/mol for Ba, 35.45 g/mol for each Cl, totaling about 208.23 g/mol for BaCl₂). Therefore:

1. 6.66 moles BaCl₂ × (208.23 g BaCl₂ / 1 mole BaCl₂) = 1386.89 g BaCl₂

So, approximately 1387 grams of the BaCl₂ hydrate would be needed to create 1.00 cup of water.