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Chapter 5: Problem 50

A compound has the empirical formula \(\mathrm{SF}_{4}\). At \(20^{\circ} \mathrm{C}, 0.100 \mathrm{~g}\) of the gaseous compound occupies a volume of \(22.1 \mathrm{~mL}\) and exerts a pressure of 1.02 atm. What is its molecular formula?

Short Answer

Expert verified
The molecular formula of the given compound is SF4.

Step by step solution

01

Calculate Empirical Formula Mass

In order to calculate empirical formula mass, you have to know the weight of each element present in the empirical formula. Here, the empirical formula is SF4. The atomic mass of sulfur (S) is 32.06 g/mol and fluorine (F) is 18.998 g/mol. So the empirical formula mass is \(32.06 g/mol + 4(18.998 g/mol) = 108.062 g/mol\)
02

Use Ideal Gas Law to find Molar Mass

The ideal gas law is given by PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. We can rearrange the formula to calculate the number of moles (n) = PV/RT. Given P is 1.02 atm, V is 22.1 mL, R is 0.0821 L·atm/K·mol and the temperature T is 20°C = 273 + 20 = 293 K. Plug these values into the rearranged formula, we have n = (1.02 atm * 22.1 mL * 1 L/1000 mL) / (0.0821 L·atm/K·mol * 293 K) = 0.000918 mol. The molar mass of the compound is obtained by dividing the mass of the sample by the number of moles, hence Molar mass = 0.100 g/0.000918 mol = 109 g/mol
03

Determining the Molecular Formula

Now, divide the molar mass by the empirical formula mass to find the number of empirical formulas in one molecule of the compound. The number is rounded to the nearest integer since a molecule cannot consist of a fraction of an atom. Hence, we have 109 g/mol / 108.062 g/mol = 1.009 ≈ 1. Since the factor is 1, the empirical and molecular formula are the same. So, the molecular formula is SF4

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Most popular questions from this chapter

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