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Chapter 3: Problem 49

A compound whose empirical formula is \(\mathrm{XF}_{3}\) consists of \(65 \%\) \(F\) by mass. What is the atomic mass of \(X\) ?

Short Answer

Expert verified
The atomic mass of element \(X\) in the compound \(\mathrm{XF_{3}}\) is approximately \(30.69 \, \text{amu}\).

Step by step solution

01

Calculate the mass of 3 F atoms

First, let's find the mass of 3 F atoms. The atomic mass of F (Fluorine) is \(19 \, \text{amu}\). We have 3 F atoms in our empirical formula, and their combined mass will be: \(3 \times 19 \, \text{amu} = 57 \, \text{amu}\).
02

Calculate the mass percentage of X in the compound

We know that the mass percentage of F in the compound is \(65 \%\). So, the mass percentage of X in the compound will be: \(100 \% - 65 \% = 35 \%\).
03

Calculate the total mass of the compound

Now let's denote the total mass of the compound as M. As we are given the mass percentages, we can write: \(\frac{57 \, \text{amu}}{\text{M}} = 0.65\). Solving for M, \(\text{M} = \frac{57 \, \text{amu}}{0.65} \approx 87.69 \, \text{amu}\).
04

Calculate the atomic mass of X

Finally, we can find the atomic mass of X. We know that 35% of the compound's mass is attributed to X: \(\frac{\text{mass of X}}{87.69 \, \text{amu}} = 0.35\). Solving for the mass of X, \(\text{mass of X} = 0.35 \times 87.69 \, \text{amu} \approx 30.69 \, \text{amu}\). Therefore, the atomic mass of element \(X\) is approximately \(30.69 \, \text{amu}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Mass
Atomic mass is a measure of the mass of an individual atom of a chemical element. It鈥檚 usually measured in atomic mass units (amu). Each element's atomic mass is roughly equal to the number of protons and neutrons it contains. For example, the atomic mass of fluorine (\(F\)) is 19 amu. This number is critical when calculating the overall mass of a compound. In our exercise, finding the atomic mass of element \(X\) requires understanding how it relates to the mass of fluorine within the compound.

Knowing the atomic mass allows us to make comparisons between elements and to calculate the molecular or empirical formulas for compounds. This is essential for understanding how different elements combine to form various chemical compounds.
Mass Percentage
Mass percentage, also known as percent composition, is used to describe the concentration of an element in a compound. It's calculated by dividing the mass of the element by the total mass of the compound and then multiplying by 100 to get a percentage. For example, if 65% of our compound's mass comes from fluorine, then 35% comes from the unknown element \(X\).

Here's how you calculate the mass percentage:
  • Determine the mass of each component in the compound.
  • Divide the mass of the individual element by the compound's total mass.
  • Multiply by 100 to get a percentage.
Mass percentage helps chemists determine the formula of a compound and identify how much of each element is present. This is crucial for the proper identification and analysis of unknown substances.
Compound Calculation
Compound calculations involve determining the total mass and the composition of a compound based on given data. In the exercise, we approached this by first finding the total mass of the compound using the mass percentages. We isolated the mass of each component, known elements like fluorine, and used the relative mass percentages to find the unknown.

Steps to follow in compound calculation:
  • Calculate the combined mass of known elements like the three fluorine atoms.
  • Use the given mass percentages to set up equations relating the total mass to the known components.
  • Solve these equations to find the total mass and then the atomic mass of the unknown element \(X\).
These calculations are vital to understanding molecular structures and ensuring the accurate synthesis and analysis of compounds in both lab and industry settings.

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Most popular questions from this chapter

\(\infty 0\) Section \(2.9\) introduced the idea of structural isomerism, with 1-propanol and 2-propanol as examples. Determine which of these properties would distinguish these two substances: (a) boiling point, (b) combustion analysis results, (c) molecular weight, (d) density at a given temperature and pressure. You can check on the properties of these two compounds in Wolfram Alpha (http://www.wolframalpha.com/) or the CRC Handbook of Chemistry and Physics. \(3.110\) A particular coal contains \(2.5 \%\) sulfur by mass. When this coal is burned at a power plant, the sulfur is converted into sulfur dioxide gas, which is a pollutant. To reduce sulfur dioxide emissions, calcium oxide (lime) is used. The sulfur dioxide reacts with calcium oxide to form solid calcium sulfite. (a) Write the balanced chemical equation for the reaction. (b) If the coal is burned in a power plant that uses 2000 tons of coal per day, what mass of calcium oxide is required daily to eliminate the sulfur dioxide? (c) How many grams of calcium sulfite are produced daily by this power plant?

A manufacturer of bicycles has 4815 wheels, 2305 frames, and 2255 handlebars. (a) How many bicycles can be manufactured using these parts? (b) How many parts of each kind are left over? (c) Which part limits the production of bicycles?

A bottling plant has 126,515 bottles with a capacity of \(355 \mathrm{~mL}\), 108,500 caps, and 48,775 L of beverage. (a) How many bottles can be filled and capped? (b) How much of each item is left over? (c) Which component limits the production?

Write balanced chemical equations corresponding to each of the following descriptions: (a) Solid calcium carbide, \(\mathrm{CaC}_{2}\), reacts with water to form an aqueous solution of calcium hydroxide and acetylene gas, \(\mathrm{C}_{2} \mathrm{H}_{2}\). (b) When solid potassium chlorate is heated, it decomposes to form solid potassium chloride and oxygen gas. (c) Solid zinc metal reacts with sulfuric acid to form hydrogen gas and an aqueous solution of zinc sulfate. (d) When liquid phosphorus trichloride is added to water, it reacts to form aqueous phosphorous acid, \(\mathrm{H}_{3} \mathrm{PO}_{3}(a q)\), and aqueous hydrochloric acid. (e) When hydrogen sulfide gas is passed over solid hot iron(III) hydroxide, the resultant reaction produces solid iron(III) sulfide and gaseous water.

The fizz produced when an Alka-Seltzer tablet is dissolved in water is due to the reaction between sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) and citric acid \(\left(\mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)\) : $$ \begin{aligned} 3 \mathrm{NaHCO}_{3}(a q)+& \mathrm{H}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \longrightarrow \\ & 3 \mathrm{CO}_{2}(g)+3 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{Na}_{3} \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}(a q) \end{aligned} $$ In a certain experiment \(1.00 \mathrm{~g}\) of sodium bicarbonate and \(1.00 \mathrm{~g}\) of citric acid are allowed to react. (a) Which is the limiting reactant? (b) How many grams of carbon dioxide form? (c) How many grams of the excess reactant remain after the limiting reactant is completely consumed?
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