Question

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

Short answer

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

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%

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)

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)

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

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.

Key concepts

Mass Percentage

In chemistry, mass percentage is used to describe the composition of a compound by calculating the percentage of a specific element's mass relative to the total mass of the compound. This is a straightforward way to express the concentration of an element in a compound.

• To find the mass percentage of an element, you divide the mass of the element by the total mass of the compound and then multiply the result by 100.
• In the problem of finding the element X in XCl extsubscript{4}, we know that chlorine (Cl) accounts for 75.0% of the compound by mass. Therefore, the mass percentage of the unknown element X is simply 100% minus the mass percentage of Cl.
• This approach helps to quickly understand how much of each element is present in a compound with respect to its total mass.

Understanding mass percentage is crucial for problems involving chemical composition, as it gives a direct insight into the quantitative composition of compounds.

Proportion Equation

A proportion equation is a powerful tool in chemistry to solve problems involving relative quantities of elements in a compound. It allows for the establishment of relationships between the percentages of each component based on their molar masses.

• In our problem, the proportion equation is formed using the known mass percentages of chlorine and X. We have two primary equations: one for chlorine, derived from its proportion of the total molar mass, and another for the unknown element X.
• By setting up a proportion equation where the molar mass of Cl is balanced against the mass percentage given (75%) and similarly for X (25%), we can solve for the unknown molar mass.
• The process involves algebraic manipulation to find the atomic mass of X, transforming information about relative mass percentages into exact values that can be used to identify unknown elements.

This method gives precise quantitative insights based on simple mass percentage representations.

Atomic Mass

Atomic mass, often synonymous with atomic weight, is the mass of an atom expressed in atomic mass units (amu). This concept is crucial for identifying elements and understanding their behavior in reactions.

• Every element on the periodic table has a characteristic atomic mass, which helps to distinguish it from other elements.
• In the exercise, to find the identity of element X, we calculated its atomic mass using the proportion equation concerning elements in the compound XCl extsubscript{4}. The expected outcome, about 47.30 g/mol, is close to the atomic mass of titanium (Ti), thus identifying X as titanium.
• Cheat-tip: always remember that atomic masses can be found on the periodic table, a fundamental tool in chemistry for these calculations.

Knowing atomic mass and applying it correctly is key in calculations and predictions related to chemical compounds.

Periodic Table

The periodic table is an indispensable resource in chemistry, organizing all known elements systematically based on their atomic number, electron configuration, and recurring chemical properties.

• It allows chemists to quickly find information like atomic mass, symbol, and more for any element.
• With regard to the problem solved, the periodic table helps us locate elements with an atomic mass around 47.30 g/mol, leading to its identification as titanium (Ti).
• This function of effortless identification makes the periodic table crucial for solving chemistry exercises, especially those requiring the determination of unknown elements like the one in this exercise.

The periodic table is not just a tool for memorizing elements, but a driver for problem-solving and understanding elements' relationships and properties.