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Chapter 3: Problem 48

The compound \(\mathrm{XCl}_{4}\) contains \(75.0 \% \mathrm{Cl}\) by mass. What is the element \(\mathrm{X} ?\)

Short Answer

Expert verified
The unknown element X in the compound XCl4 is titanium (Ti), making the compound TiCl4, which is titanium(IV) chloride. The molar mass of the unknown element X is found to be approximately 47.30 g/mol, which corresponds to titanium's molar mass of around 47.87 g/mol.

Step by step solution

01

Calculate the mass percentage of the unknown element X

The compound XCl4 contains 75.0% Cl by mass. Since there are only two elements in the compound, the mass percentage of the unknown element X can be found using: Mass percentage of X = 100% - Mass percentage of Cl Mass percentage of X = 100% - 75.0% = 25.0%
02

Write down the molar mass percentages

Let Mx be the molar mass of the unknown element X. Then, we can write down the molar mass percentages using the atomic masses of Cl and X: Molar mass of XCl4 = Mx + 4 * (Molar mass of Cl) Since there are four chlorine atoms in the compound, their combined molar mass percentage would be: 4 * (Molar mass of Cl) / (Molar mass of XCl4) = 0.750 (since it is 75% by mass)
03

Set up the proportion equation

Using the mass percentage of the unknown element X and the molar mass percentage of Cl, we can set up a proportion equation: (Molar mass of X) / (Molar mass of XCl4) = 0.250 (since it is 25% by mass)
04

Solve the equation for the atomic mass of X

Substituting the values from Step 2 into the equation, we get: Mx / (Mx + 4 * (Molar mass of Cl)) = 0.250 Now, we know that the molar mass of Cl is 35.45 g/mol. Insert this value into the equation and solve for Mx: Mx / (Mx + 4 * 35.45) = 0.250 After solving the equation, we find the molar mass of the unknown element X to be: Mx ≈ 47.30 g/mol
05

Identify the unknown element X

With a molar mass of approximately 47.30 g/mol, we can check the periodic table for an element with a molar mass close to this value. The element with a similar molar mass is titanium (Ti), with a molar mass of around 47.87 g/mol. Therefore, the unknown element X is titanium (Ti). In conclusion, the compound XCl4 is actually TiCl4, which is titanium(IV) chloride.

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Most popular questions from this chapter

Balance the following equations and indicate whether they are combination, decomposition, or combustion reactions: (a) \(\mathrm{C}_{3} \mathrm{H}_{6}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{N}_{2} \mathrm{O}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{C}_{5} \mathrm{H}_{6} \mathrm{O}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)\) (d) \(\mathrm{N}_{2}(g)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{NH}_{3}(g)\) (e) \(\mathrm{K}_{2} \mathrm{O}(s)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{KOH}(a q)\)

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