Video Transcript
A student believes that the chemical formula of a hydrated compound of cobalt sulfate is CoSO4 7H2O. If the student were to heat a 2.56-gram sample of this compound, what mass of water would be lost from the sample? Give your answer to two decimal places. The molar mass of cobalt is 59 grams per mole, sulfur is 32 grams per mole, oxygen is 16 grams per mole, and hydrogen is one gram per mole.
A hydrated compound or salt is a substance that contains water of crystallization. In other words, water molecules are part of its crystal structure. We can see from the chemical formula that each unit of cobalt(II) sulfate has seven molecules of water associated with it. If we were to heat up the hydrated salt, we could remove the water of crystallization to leave behind a substance that does not contain water. This is known as an anhydrous salt.
In this question, we need to calculate how much water would be lost if we were to heat 2.56 grams of the hydrated salt. We will assume that water is the only type of molecule lost from the salt when it is heated and that all of the water of crystallization is lost. One way we can solve this problem is to determine the percentage by mass of water molecules present in the hydrated salt. Then, we can use this percentage to calculate the mass of the sample that corresponds to only the water of crystallization that would be lost.
In order to calculate the percentage by mass of water, we must calculate the molar mass of just the water of crystallization, divide it by the molar mass of the entire hydrated salt, and then multiply by 100 percent. To find the molar mass of water, we multiply the average molar mass of hydrogen by two and add this to the average molar mass of oxygen, which gives us 18 grams per mole. However, the chemical formula for the hydrated salt contains seven moles of water. So we need to multiply this number by seven. Therefore, the molar mass of the water in the hydrated salt is 126 grams per mole.
Next, we need to calculate the molar mass of the entire hydrated salt. Since we have already calculated the water portion of the hydrated salt, we only need to calculate the molar mass of cobalt(II) sulfate. We can calculate the molar mass of cobalt(II) sulfate by adding together the average molar masses of cobalt, sulfur, and four times the average molar mass of oxygen. This gives us 155 grams per mole. After adding together the molar masses of the water and the salt, we find that the molar mass of the entire hydrated salt is 281 grams per mole.
Now we’re ready to calculate the percentage by mass of water in the hydrated salt. Dividing 126 grams per mole by 281 grams per mole gives us the percentage by mass of water in the hydrated salt. This is the percentage of the mass of the sample that would be lost as water if the hydrated salt was heated.
To find the mass of water lost, let’s take the decimal equivalent of this percentage and multiply it by the mass of the hydrated salt that was given in the problem, which was 2.56 grams. Finally, we need to round our answer to two decimal places. The result is 1.15 grams of water.
In conclusion, the mass of water that would be lost when 2.56 grams of the cobalt(II) sulfate hydrate in the problem is heated is 1.15 grams.
