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Chapter 3: Problem 41

A compound \(\mathrm{XCl}_{3}\) is \(70.3 \%\) (by mass) chlorine. What is the molar mass of the compound? What is the symbol and name of X?

Short Answer

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Question: Given a compound XCl3, where chlorine makes up 70.3% of the mass, find the molar mass of the compound and identify the element X. Answer: To calculate the molar mass of the compound XCl3, first determine the mass of the three chlorine atoms and the unknown element X. Then, add the molar mass of X to the molar mass of three chlorine atoms. Finally, identify the unknown element X based on its molar mass found in the periodic table.

Step by step solution

01

Determine the mass of chlorine in the compound

If chlorine makes up 70.3% of the mass of the compound XCl3, then we can find the mass of chlorine as: Mass of chlorine (g) = (\(70.3 \times \mathrm{mass\, of\, the\, compound\,} (g))/100\)
02

Determine the mass of the unknown element X

Using the percentage mass of chlorine, we can find the percentage mass of the unknown element X as 100% - 70.3% = 29.7%. Thus, the mass of the unknown element X (g) can be calculated as follows: Mass of X (g) = (\(29.7 \times \mathrm{mass\, of\, the\, compound\,} (g))/100\)
03

Determine the molar mass of the compound XCl3

We know that there are three chlorine atoms in the compound XCl3. The molar mass of one chlorine atom is 35.45 g/mol. Therefore, the molar mass of three chlorine atoms is: \(3 \times 35.45\,\mathrm{g/mol} = 106.35\,\mathrm{g/mol}\) Next, we will use the mass of the unknown element X we found in step 2 and divide it by the molar mass of the three chlorine atoms: Molar mass of X = (Mass of X (g))/(106.35 g/mol)
04

Identify element X based on its molar mass

Once we have calculated the molar mass of the unknown element X, we can use the periodic table to identify the element based on its atomic mass. For example, if the molar mass of X is close to 118.71 g/mol, then the element X is tin (Sn).
05

Calculate the molar mass of the compound XCl3

Now that we have identified the unknown element X, we can calculate the molar mass of the compound XCl3 by adding the molar mass of X to the molar mass of the three chlorine atoms: Molar mass of XCl3 = Molar mass of X + Molar mass of 3 Cl

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