Question Video: Finding the Number of Molecules in a Hydrate from the Mass of the Hydrate and Water | Nagwa Question Video: Finding the Number of Molecules in a Hydrate from the Mass of the Hydrate and Water | Nagwa

Question Video: Finding the Number of Molecules in a Hydrate from the Mass of the Hydrate and Water Chemistry • Third Year of Secondary School

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A sample of cobalt(II) chloride hydrate (CoCl₂⋅𝑥H₂O) is heated until its mass remains constant. For every 1.00 g of cobalt(II) chloride produced, 0.831 of water is liberated. What is the value of 𝑥, where 𝑥 is an integer? [Co = 59 g/mol, cl = 35.5 g/mol, H = 1 g/mol, O = 16 g/mol]

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Video Transcript

A sample of cobalt(II) chloride hydrate CoCl2⋅𝑥H2O is heated until its mass remains constant. For every 1.00 grams of cobalt(II) chloride produced, 0.831 grams of water is liberated. What is the value of 𝑥, where 𝑥 is an integer? And we are given the molar mass of cobalt, 59 grams per mole; for chlorine, 35.5 grams per mole; for hydrogen, one gram per mole; and oxygen, 16 grams per mole.

We are told that a hydrated salt, cobalt(II) chloride, is heated until constant mass. The name cobalt(II) chloride hydrate and the formula do not tell us how many molecules of water they are per unit of cobalt chloride. We are only told the number of moles of water of crystallization in terms of x. Heating a hydrated salt to constant mass typically involves heating a salt strongly in a crucible with the lid off to allow the water of crystallization to escape.

The reaction equation for this process is CoCl2⋅𝑥H2O solid being heated to give CoCl2 solid plus 𝑥H2O gas. Over time, all the water of crystallization is removed. The hydrated salt is converted to an anhydrous salt. An anhydrous salt contains no water of crystallization. During cooling and weighing, the lid of the crucible must be in place, and this is to prevent water vapor from the air reentering the crucible.

This is important because this reaction is reversible, and we want to prevent the reverse reaction from occurring. Otherwise, the masses of each substance are unknown. We need to ensure that cobalt(II) chloride is indeed fully anhydrous. To solve this problem, we can put the data that we are given and that which we need to find into a table. This table is not absolutely necessary, but sometimes it helps when we are dealing with a lot of information.

We are told that for every 1.00 grams of cobalt(II) chloride produced, so let’s put this mass into the table under CoCl2, 0.831 grams of water is liberated. And so, this is the mass of water. The words “for every” tell us that 1.00 grams of cobalt(II) chloride and 0.831 grams of water are not necessarily the actual masses of these substances produced, but rather the ratio in which they are produced.

We know that the stoichiometric coefficients one as to 𝑥 is the mole ratio of these substances. So first, we need to convert the masses of these products to moles. We start by calculating the molar mass of cobalt(II) chloride, which is equal to the molar mass of cobalt plus two times the molar mass of chlorine since there are two chlorines. Substituting in the molar mass of cobalt, which was given to us 59 grams per mole, and that of chlorine, 35.5 grams per mole, we get a molar mass of cobalt(II) chloride of 130 grams per mole. We can put this value into the table.

The molar mass of water is equal to two times the molar mass of hydrogen because there are two hydrogens plus the molar mass of oxygen, and these values are given to us. So, substituting one gram per mole for hydrogen and 16 grams per mole for oxygen, we get 18 grams per mole, the molar mass of water, which we can put into the table.

The next step is to calculate the number of moles of cobalt(II) chloride and water. We can use the key equation number of moles is mass divided by molar mass. So, for cobalt(II) chloride, taking its mass and molar mass from the table, we get 1.00 grams divided by 130 grams per mole, which is equal to 0.00769 moles. For water, the number of moles is equal to its mass, 0.831 grams, divided by its molar mass, 18 grams per mole, which gives 0.04616 moles.

Since the ratio of the moles of cobalt(II) chloride as to water are the same as the stoichiometric ratio one as to 𝑥, we can now solve for 𝑥. How we do this is we take the moles of cobalt(II) chloride as to the moles of water and divide each value by the moles of cobalt(II) chloride. These two values cancel, giving us one. The moles units cancel on both sides, and solving this division here, we get 6.00166.

So far, in this calculation, we have not rounded off, but now it is time to do so. We need to round off to a value with no decimal places since 𝑥 cannot be a fraction. We cannot have a fraction of a water molecule. And we are specifically told that 𝑥 is an integer. Finally, we get an answer of one as to six. And this is the mole ratio of cobalt chloride as to water. These values are also the coefficients in the hydrated compound formula. Therefore, the value of 𝑥 is six. And the formula of the hydrated compound is CoCl2⋅6H2O, which is cobalt(II) chloride hexahydrate.

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