Question Video: Calculating the Percentage by Mass of Water in Alum Given Its Chemical Formula | Nagwa Question Video: Calculating the Percentage by Mass of Water in Alum Given Its Chemical Formula | Nagwa

# Question Video: Calculating the Percentage by Mass of Water in Alum Given Its Chemical Formula Chemistry • Third Year of Secondary School

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Alum is a hydrated sulfate of potassium and aluminum with the chemical formula KAl(SO₄)₂⋅12H₂O. What is the percentage by mass of water in alum? Give your answer to two decimal places. [K = 39 g/mol, Al = 27 g/mol, S = 32 g/mol, O = 16 g/mol, H = 1 g/mol]

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### Video Transcript

Alum is a hydrated sulfate of potassium and aluminum with the chemical formula KAl(SO4)2•12H2O. What is the percentage by mass of water in alum? Give your answer to two decimal places. The molar mass of potassium is 39 grams per mole, aluminum is 27 grams per mole, sulfur is 32 grams per mole, oxygen is 16 grams per mole, and hydrogen is one gram per mole.

In this question, we want to know the percentage by mass of water in alum. The question states that alum is a hydrated salt. A hydrated salt is a salt that has water incorporated into its crystal lattice. The presence of water molecules within the crystal structure of a compound is known as the water of crystallization.

If we look at the chemical formula of alum, we can see that for each formula unit of the salt, there are 12 molecules of water. It is the presence of these molecules of water which tells us this is a hydrated salt.

If we did an experiment and heated the hydrated salt, we could find the mass of water that was lost during heating. Since we are not given experimental data in this question, we need to use the molar masses of the water of crystallization and the hydrated salt instead. Let’s first calculate the total molar mass of water present in the hydrated salt.

The molar mass of water can be calculated by adding together the average molar masses of its constituent atoms. Each water molecule contains two hydrogen atoms and one oxygen atom. So using the average molar masses provided in the problem, we find that the molar mass of water is 18 grams per mole. Since there are 12 molecules of water in alum, we need to multiply the molar mass of water by 12. The answer is 216 grams per mole.

Now let’s calculate the molar mass of the entire hydrated salt. We have already calculated the molar mass of the water of crystallization, so all that remains is the molar mass of the potassium aluminum sulfate. The average molar mass of potassium is 39 grams per mole, and the average molar mass of aluminum is 27 grams per mole. We need to multiply the average molar mass of sulfur by two because there are two sulfur atoms in the chemical formula. Finally, we need to multiply the average molar mass of oxygen by eight because, excluding water, there are eight oxygen atoms in the chemical formula.

Now we need to add together the molar masses of potassium, aluminum, sulfur, oxygen, and water. Therefore, the total molar mass of alum is 474 grams per mole.

Now we’re ready to calculate the percentage by mass of water in alum. Let’s divide the molar mass of the water, which is 216 grams per mole, by the total molar mass of alum, which is 474 grams per mole. After multiplying by 100, our answer is approximately 45.5696 percent. However, we need to round our answer to two decimal places. In conclusion, the percentage by mass of water in alum is 45.57 percent.

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