Question

Two compounds of $\mathrm{Cl}$ and $\mathrm{X}$ are found to have molecular masses and \% Cl, by mass, as follows: 137 u, $77.5\mathrm{\%}\mathrm{Cl};208\mathrm{u},85.1\mathrm{\%}$ Cl. What is element $\mathrm{X}?$ What is the formula for each compound?

Short answer

The element X is Lead (Pb) with atomic mass of about 207.2. The formulas for the compounds are PbCl2 and PbCl4.

Step-by-step solution

Convert percentages to mass

First, convert the percentages of Cl to mass for both compounds using the given molecular masses. For the first compound: $(77.5/100)\times 137$ u, and for the second compound: $(85.1/100)\times 208$ u.

Determine mass of X

Then, determine the mass of element X in each compound by subtracting the mass of Cl from the total molecular mass. Do this for both compounds.

Identify the Element X

Next, use the periodic table to identify which element has approximately the calculated atomic mass. This is your unknown element X.

Determine the Ratio of Cl to X

Finally, determine the ratio of the number of Cl atoms to X atoms in each compound to confirm the molecular formula. Do this by taking the mass of each element, dividing by its atomic mass to get the number of moles, and then finding the ratio of Cl:X.

Key concepts

Molecular Mass Calculation

Molecular mass is the sum of the atomic masses of all the atoms in a molecule. To calculate it, multiply the atomic mass of each element by the number of times it appears in the compound, and then add these values together.
For example, if a compound consists of two chlorine atoms (each with an atomic mass of approximately 35.5 u) and one other element, the total contribution from chlorine would be 2 x 35.5 = 71 u.
This is a fundamental step because it helps to understand the proportion of each element in the compounds.

Percentage Composition

Percentage composition tells us the percentage of each element in a compound. Knowing this helps in determining the formula of the compound and understanding its makeup.
To calculate the percentage composition of a particular element, divide the total mass of that element in the compound by the molecular mass of the compound and multiply by 100.
For example, if a compound's molecular mass is 137 u and contains 77.5% chlorine, then 77.5% of 137 u gives the mass of chlorine in the compound.

• This calculation helps quantify each part of the compound in easily understandable terms.

Chemical Formula Determination

Chemical formula determination involves translating the mass data into an empirical or molecular formula. This requires the ratio of the number of atoms of each element in the compound.
After calculating the percentage composition, use the periodic table to find the atomic masses. Divide the mass of each element by its atomic mass to find the number of moles.
Convert the moles into a ratio to determine the simplest whole numbers of atoms in the formula.
This step ensures we represent the compound with the correct formula, important for understanding its chemical behavior.

Periodic Table Utilization

The periodic table is an essential tool for identifying elements based on atomic mass, which is crucial when determining unknown components of a compound.
Using the periodic table, you can match calculated masses to atomic masses of known elements, helping identify the mysterious 'X.'
It's like a map, guiding you through the atomic landscape to find precise values needed for calculations.
Effective use of the periodic table ensures accurate identification and understanding of elements and their properties.