Question Video: Determining the Identity of a Metal in a Hydrated Salt Using Experimental Data | Nagwa Question Video: Determining the Identity of a Metal in a Hydrated Salt Using Experimental Data | Nagwa

# Question Video: Determining the Identity of a Metal in a Hydrated Salt Using Experimental Data Chemistry • Third Year of Secondary School

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An unknown hydrated metal salt has the chemical formula XBr₂⋅6H₂O. When a 4.361 g sample of the salt is heated, the sample decreases in mass by 1.443 g. Which of the following is the identity of metal X? [Br = 80 g/mol, H = 1 g/mol, O = 16 g/mol] [A] Co [M = 59 g/mol] [B] Cu [M = 63.5 g/mol] [C] Fe [M = 56 g/mol] [D] V [M = 51 g/mol] [E] Mn [M = 55 g/mol]

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### Video Transcript

An unknown hydrated metal salt has the chemical formula XBr2⋅6H2O. When a 4.361-gram sample of the salt is heated, the sample decreases in mass by 1.443 grams. Which of the following is the identity of metal X? The molar mass of bromine is 80 grams per mole, hydrogen is one gram per mole, and oxygen is 16 grams per mole. (A) Co, M equals 59 grams per mole. (B) Cu, M equals 63.5 grams per mole. (C) Fe, M equals 56 grams per mole. (D) V, M equals 51 grams per mole. (E) Mn, M equals 55 grams per mole.

Let’s start by defining a hydrated metal salt in order to understand what happens when it is heated. When a salt contains molecules of water as part of its structure, it’s known as a hydrated salt. During a volatilization gravimetry experiment, if we are able to remove all the water molecules from the hydrated salt by heating, we would form the anhydrous salt. This is why the mass of the anhydrous salt is less than the hydrated salt. The mass of the liberated water molecules is simply calculated as the difference between the mass of the sample before heating and the mass of the sample after heating.

The mass of the water lost from the hydrated salt is given in the question as 1.443 grams. And the mass of the sample before heating is given as 4.361 grams. Therefore, we can calculate the mass of the anhydrous salt by subtracting 1.443 grams from 4.361 grams. This gives us 2.918 grams. We can now use this information to help us figure out the identity of X. First, we need to convert 1.443 grams of water to moles. Next, we will find the number of moles of XBr2. Finally, we will determine the molar mass of X, which will help us identify the metal.

The number of moles of water can be calculated by using the following formula. The number of moles equals the mass in grams divided by the molar mass in grams per mole. The mass of water is 1.443 grams, and the molar mass of water is 18 grams per mole. The molar mass of water is calculated by adding together the average molar masses of two hydrogen atoms and one oxygen atom. Dividing 1.443 grams by 18 grams per mole gives us the number of moles of water. Now, to determine the number of moles of XBr2, we need to look at the provided chemical formula of the hydrated salt. From the formula, we can determine that there are six moles of water per every one mole of XBr2. We can therefore calculate the number of moles of XBr2 by dividing the number of moles of water by six.

Now that we have the number of moles and the mass of the anhydrous salt XBr2, we can calculate its molar mass. The molar mass can be calculated by dividing the mass in grams by the number of moles. After substituting in the correct values and dividing, we obtain the molar mass of XBr2. Since we want to know the molar mass of just X, we need to take the molar mass of XBr2 and subtract the molar mass of Br2. The average molar mass of Br is 80 grams per mole. So the molar mass of Br2 is 160 grams per mole. After subtracting 160 grams per mole from the molar mass of XBr2, we finally have the molar mass of X.

When looking at the answer choices, we can see that the metal that has a molar mass closest to the one we calculated is cobalt. Therefore, the identity of metal X is cobalt, which has an average molar mass of 59 grams per mole.

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