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Chapter 6: Problem 38

A 2.650 g sample of a gaseous compound occupies \(428 \mathrm{mL}\) at \(24.3^{\circ} \mathrm{C}\) and \(742 \mathrm{mmHg} .\) The compound consists of \(15.5 \%\) C \(, 23.0 \%\) Cl, and \(61.5 \%\) F, by mass. What is its molecular formula?

Short Answer

Expert verified
The molecular formula of the compound is \(C_4Cl_2F_{10}\).

Step by step solution

01

Calculate the molar mass of the compound

The molar mass can be calculated using the ideal gas law \(PV=nRT\) where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in kelvins. Rewriting this equation for n, we get \(n=PV/RT\). First, convert temperature from Celsius to Kelvins by adding 273. Then, convert the pressure from mmHg to atm by dividing it by 760. Finally, calculate n by substituting P \(=742/760=0.976\) atm, V=0.428L, R=0.0821 L.atm/mol.K, and T=24.3+273=297.3K into the equation. This gives n=\(0.976*0.428/0.0821*297.3=0.011\) moles. The molar mass is then given by the ratio mass/n, which is \(2.650/0.011=240.9\) g/mol.
02

Calculate the empirical formula

Calculate the mass of each element in the compound using the given percentages. This yields 0.410 g C, 0.6095 g Cl, and 1.630 g F. Divide these masses by their atomic masses to get the number of moles of each element: \(0.410/12.01=0.0341\) moles C, \(0.6095/35.45=0.0172\) moles Cl, and \(1.630/18.998=0.0857\) moles F. Divide these numbers of moles by the smallest one to get the ratio of atoms in the empirical formula. This gives C2ClF5. So the empirical formula is \(C_2ClF_5\).
03

Determine the molecular formula

The molecular formula is a multiple of the empirical formula. Calculate the molar mass of the empirical formula, which is \(2*12.01+35.45+5*18.998=120.45\) g/mol. Divide the molar mass of the compound by the molar mass of the empirical formula to get the multiple, which is \(240.9/120.45=2\). So the molecular formula is \(C_4Cl_2F_{10}\).

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Most popular questions from this chapter

At times, a pressure is stated in units of mass per unit area rather than force per unit area. Express \(P=1 \mathrm{atm}\) in the unit \(\mathrm{kg} / \mathrm{cm}^{2}\) [Hint: How is a mass in kilograms related to a force?]

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A constant-volume vessel contains \(12.5 \mathrm{g}\) of a gas at 21 ^ C. If the pressure of the gas is to remain constant as the temperature is raised to \(210^{\circ} \mathrm{C}\), how many grams of gas must be released?

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