Problem 41 - Chemistry: Principles and Reactions

Question

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?

Step-by-Step Solution

Answer

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 1: 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) = (\(70.3 \times \mathrm{mass\, of\, the\, compound\,} (g))/100\)

Step 2: 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) = (\(29.7 \times \mathrm{mass\, of\, the\, compound\,} (g))/100\)

Step 3: 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)

Step 4: 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).

Step 5: 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

Key Concepts

Molar Mass Calculation

Understanding the calculation of molar mass is key to this exercise. The molar mass of a compound is determined by adding the atomic masses of all the atoms present in a molecule of the compound. For the compound \(\mathrm{XCl}_3\), we have three chlorine atoms. The atomic mass of chlorine is \(35.45\,\mathrm{g/mol}\), so for three atoms, we multiply by three: \[ 3 \times 35.45\,\mathrm{g/mol} = 106.35\,\mathrm{g/mol} \]To find the total molar mass of the compound, we need to include the molar mass of the unknown element \(\mathrm{X}\). First, calculate the contribution of chlorine to the molar mass by using the percentage composition provided. Then, subtract this value from the total molar mass to isolate the contribution from \(\mathrm{X}\).To determine the molar mass of \(\mathrm{X}\), use the formula:\[\text{Molar mass of } \mathrm{X} = \frac{\text{Mass of } \mathrm{X} (\mathrm{g})}{106.35\,\mathrm{g/mol}}\]Once you know the molar mass of \(\mathrm{X}\), adding it to that of three chlorine atoms gives you the molar mass of the compound.

Percentage Composition

Percentage composition refers to the percentage by mass of each element in a compound. In this exercise, we're given that the compound \(\mathrm{XCl}_3\), chlorine contributes \(70.3\%\) of its mass. This percentage helps us understand how much of the compound's molar mass is due to chlorine. By applying this percentage, we can easily pinpoint the mass contribution from both chlorine and the unknown element \(\mathrm{X}\).To find the percentage composition of \(\mathrm{X}\) in the compound, simply subtract chlorine's percentage from \(100\%\):\[ 100\% - 70.3\% = 29.7\% \]This calculation shows that \(29.7\%\) of the compound's mass is from \(\mathrm{X}\).Such information allows us to calculate the actual mass of each element within any given sample of the compound. Knowing one element's contribution percentage lets us deduce unknown values easily with logical steps.

Periodic Table Identification

The periodic table is a crucial tool for chemists, allowing them to identify elements based on atomic number and molar mass. In problems like this one, once the molar mass of the unknown element \(\mathrm{X}\) has been calculated, the periodic table can help identify the element by matching the closest atomic mass. For example, if the molar mass of \(\mathrm{X}\) computed from the exercise is about \(118.71\,\mathrm{g/mol}\), quick reference to the periodic table shows this corresponds to tin (Sn).The periodic table also provides valuable information like:

• Atomic number, which indicates the number of protons in an atom.
• Elemental symbol, simplifying chemical notation.
• Group and period, aiding in understanding chemical properties.

This step completes the analysis of the compound. By integrating the molar mass calculation and periodic table information, we can easily identify unknown elements in chemical compositions.