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Chapter 3: Problem 161

An element \(\mathrm{X}\) forms both a dichloride \(\left(\mathrm{XCl}_{2}\right)\) and a tetrachloride \(\left(\mathrm{XCl}_{4}\right) .\) Treatment of \(10.00 \mathrm{~g} \mathrm{XCl}_{2}\) with excess chlorine forms \(12.55 \mathrm{~g} \mathrm{XCl}_{4}\). Calculate the atomic mass of \(\mathrm{X}\), and identify \(\underline{X}\)

Short Answer

Expert verified
The atomic mass of element X is approximately 32 g/mol, and the element is sulfur (S).

Step by step solution

01

1. Determine the mass of chlorine in the XCl2 compound

First, let's find out the mass of chlorine in the dichloride compound (XCl2). As there are two chlorine atoms in XCl2, we can determine the mass of chlorine as 2 times the atomic mass of chlorine. The atomic mass of chlorine is 35.45 g/mol. Therefore, the mass of chlorine in XCl2 is: \(2\times35.45 g/mol\)= 70.90 g/mol
02

2. Write the conservation of mass equation

Next, we'll write the conservation of mass equation. We know that the mass of XCl2 plus the mass of the added chlorine equals the mass of XCl4. Let Mx be the atomic mass of X, then we have: Mass of XCl2 + Mass of added Cl2 = Mass of XCl4
03

3. Find the mass of added chlorine

Let's find the mass of added Cl2 to form XCl4 from XCl2. We know the mass of the product (XCl4) and the mass of the reactant (XCl2). The difference between these two masses will be the mass of added Cl2. Mass of added Cl2 = Mass of XCl4 - Mass of XCl2 = 12.55 g - 10.00 g = 2.55 g
04

4. Determine the moles of Cl2 added

To find the moles of Cl2 added, we can use the molar mass of Cl2. The atomic mass of chlorine is 35.45 g/mol, and since Cl2 has 2 chlorine atoms, the molar mass of Cl2 is 2 times the atomic mass of chlorine: Molar mass of Cl2 = 2 x 35.45 g/mol = 70.90 g/mol Now, find the moles of Cl2 added: Moles of Cl2 added = (Mass of added Cl2) / (Molar mass of Cl2) = 2.55 g / 70.90 g/mol = 0.036 moles
05

5. Calculate the moles of X present in XCl2

Since in the XCl2 compound, there is one atom of X for every 2 atoms of Cl, the number of moles of X in XCl2 will be equal to the moles of Cl2 added. Moles of X = Moles of Cl2 added = 0.036 moles
06

6. Calculate the atomic mass of X

We can use the moles of X to find its atomic mass. Rearranging the conservation of mass equation in terms of atomic mass of X: Mx = (Mass of XCl2 - Mass of Cl2 in XCl2) / Moles of X Mx = (10.00 g - (2 x 35.45 g/mol x 0.036 moles)) / 0.036 moles Mx ≈ 32 g/mol
07

7. Identify element X

Now that we have the atomic mass of X, we can identify the element. An element with an atomic mass close to 32 g/mol is sulfur. Thus, the element X is sulfur (S). In conclusion, the atomic mass of element X is approximately 32 g/mol, and the element is sulfur (S).

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Most popular questions from this chapter

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