Laboratory ammonia is 14.3 M with a density of 0.898 g/mL. What is the mole fraction of ammonia in this solution?
- 0.2806 moles
- 0.1021 moles
- 0.9874 moles
- None of these
Explanation
To find the mole fraction of ammonia, we need to know the number of moles of ammonia and the total number of moles of all components in the solution.
Given:
Molarity of ammonia = 14.3 M
Density of solution = 0.898 g/mL
First, let's find the mass of 1 liter of the solution:
Mass = Density x Volume
= 0.898 g/mL x 1000 mL
= 898 g
Now, let's find the number of moles of ammonia in 1 liter of the solution:
Number of moles = Molarity x Volume (in liters)
= 14.3 M x 1 L
= 14.3 mol
The molar mass of ammonia (NH3) is approximately 17.03 g/mol. So, the mass of ammonia in 1 liter of the solution is:
Mass of ammonia = Number of moles x Molar mass
= 14.3 mol x 17.03 g/mol
= 243.64 g
Now, let's find the mass of water in 1 liter of the solution:
Mass of water = Total mass - Mass of ammonia
= 898 g - 243.64 g
= 654.36 g
The molar mass of water (H2O) is approximately 18.02 g/mol. So, the number of moles of water in 1 liter of the solution is:
Number of moles = Mass / Molar mass
= 654.36 g / 18.02 g/mol
= 36.33 mol
Now, we can find the mole fraction of ammonia:
Mole fraction = Number of moles of ammonia / Total number of moles
= 14.3 mol / (14.3 mol + 36.33 mol)
= 0.2806
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