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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 the molecular formula of the gas?

Short Answer

Expert verified
In order to find the molecular formula, calculate the number of moles using the ideal gas law. Then, calculate molar mass using the given weight and the moles that was first calculated. Following this, calculate empirical formula mass. Lastly, find the molecular formula by dividing the molar mass by empirical formula mass. Multiply all subscripts in the empirical formula by this number.

Step by step solution

01

Calculation of moles using Ideal Gas Law

To find the molecular formula, we first need to calculate the number of moles in the sample. The ideal gas law equation is \(PV=nRT\), where: P=pressure (in atmosphere), V=volume (in litres), n=number of moles, R=gas constant (0.0821 L.atm/K.mol) and T=temperature (in Kelvin). Convert the given temperature to Kelvin by adding 273 to the Celsius temperature, hence \(T=20+273=293K\). Substituting the given pressure, volume and converted temperature into the Ideal gas law, solve the equation for n.
02

Calculating Molar Mass

Now that we know the number of moles (\(n\)), we can calculate the molar mass. The molar mass of a substance is the mass of one mole of that substance. We can calculate it using the formula, molar mass = mass of the sample in grams/n, where mass of the sample in grams is given as 0.100 g. Now, substitute the moles calculated in step 1 into this formula and calculate the molar mass.
03

Calculation of Empirical Formula Mass

The next step is to calculate the empirical formula mass. For SF4, the empirical formula mass is determined by counting the atomic masses of all atoms in the molecule, which gives: \[Empirical formula mass = 1 * (Atomic mass of S)+ 4 * (Atomic mass of F)\]
04

Calculation of Molecular Formula

Divide the molar mass from step 2 by the empirical formula mass from step 3. This gives the number of empirical formulas in each molecule. Round this number to the nearest whole number, as it should be a whole number. The molecular formula is found by multiplying all subscripts in the empirical formula by this number.

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Most popular questions from this chapter

Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is \(0.0050 \mathrm{~cm}\) and the air inside contains 14 percent oxygen. Assuming that the pressure in the alveoli is 1.0 atm and the temperature is \(37^{\circ} \mathrm{C},\) calculate the number of oxygen molecules in one of the alveoli.

The empirical formula of a compound is \(\mathrm{CH}\). At \(200^{\circ} \mathrm{C}, 0.145 \mathrm{~g}\) of this compound occupies \(97.2 \mathrm{~mL}\) at a pressure of 0.74 atm. What is the molecular formula of the compound?

Identify the gas whose root-mean-square speed is 2.82 times that of hydrogen iodide (HI) at the same temperature.

In 2012 , Felix Baumgartner jumped from a balloon roughly \(24 \mathrm{mi}\) above Earth, breaking the record for the highest skydive. He reached speeds of more than 700 miles per hour and became the first skydiver to exceed the speed of sound during free fall. The helium-filled plastic balloon used to carry Baumgartner to the edge of space was designed to expand to \(8.5 \times 10^{8} \mathrm{~L}\) in order to accommodate the low pressures at the altitude required to break the record. (a) Calculate the mass of helium in the balloon from the conditions at the time of the jump \((8.5 \times\) \(\left.10^{8} \mathrm{~L},-67.8^{\circ} \mathrm{C}, 0.027 \mathrm{mmHg}\right) .\) (b) Determine the volume of the helium in the balloon just before it was released, assuming a pressure of 1.0 atm and a temperature of \(23^{\circ} \mathrm{C}\).

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