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Chapter 1: Problem 19

Select the correct alternative from the given choices. \(20 \mathrm{cc}\) of a hydrocarbon on complete combustion gave \(80 \mathrm{cc}\) of \(\mathrm{CO}_{2}\) and \(100 \mathrm{cc}\) of \(\mathrm{H}_{2} \mathrm{O}\) at \(\mathrm{STP}\). The empirical formula of that compound is (a) \(\mathrm{C}_{2} \mathrm{H}_{5}\) (b) \(\mathrm{C}_{2} \mathrm{H}_{6}\) (c) \(\mathrm{C}_{3} \mathrm{H}_{8}\) (d) \(\mathrm{C}_{4} \mathrm{H}_{10}\)

Short Answer

Expert verified
a) CH b) C2H4 c) C3H8 d) CH4 Answer: c) C3H8

Step by step solution

01

Calculate the moles of CO₂ and H₂O produced

To do this, we will use the molar volume of an ideal gas at standard temperature and pressure (STP), which is 22.4 liters (L) or 22,400 cc per mole. Therefore, we can calculate the moles of CO₂ and H₂O as: Moles of CO₂ = \(\frac{80 \,\text{cc}}{22,400 \,\text{cc/mol}}\) Moles of H₂O = \(\frac{100 \,\text{cc}}{22,400 \,\text{cc/mol}}\)
02

Determine the moles of carbon and hydrogen in the initial hydrocarbon

Since CO₂ is produced by the combustion of carbon, the moles of CO₂ can be used to calculate moles of carbon in the hydrocarbon: Moles of C = Moles of CO₂ For hydrogen, we know that a H₂O molecule has two hydrogen atoms. Therefore, moles of hydrogen can be calculated as: Moles of H = 2 × Moles of H₂O
03

Calculate the C-to-H mole ratio

Now that we have the moles of C and H in the initial hydrocarbon, we can find the simplest whole number ratio between them by dividing each by their respective moles: C-to-H ratio = \(\frac{\text{Moles of C}}{\text{Moles of H}}\)
04

Determine the empirical formula

Based on the C-to-H ratio, we can now choose the correct empirical formula from the given options. After performing the calculations: Moles of CO₂ = \(\frac{80}{22,400}\) = 0.00357 moles Moles of H₂O = \(\frac{100}{22,400}\) = 0.00446 moles Moles of C = 0.00357 moles Moles of H = 2 × 0.00446 = 0.00893 moles C-to-H ratio = \(\frac{0.00357}{0.00893}\) = 0.40 (approximately) The closest whole number ratio of C-to-H is 1:3 (C3H8). Therefore, the correct answer is (c) \(\text{C}_3\text{H}_8\).

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Most popular questions from this chapter

Fill in the blanks. Pressure exerted by water vapour in moist gas is called

State whether the following statements are true or false. When a \(200 \mathrm{ml}\) gas, in a closed vessel, is heated to \(50^{\circ} \mathrm{C}\) from \(25^{\circ} \mathrm{C}\), the volume becomes doubled.

Select the correct alternative from the given choices. \(44 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) contains (a) 2 moles of oxygen atoms (b) 1 mole of oxygen atoms (c) \(1.5\) moles of oxygen atoms (d) 2 moles of oxygen molecules

Select the correct alternative from the given choices. When one mole each of \(\mathrm{CO}\) and \(\mathrm{O}_{2}\) are made to react at STP, the total number of moles at the end of the reaction is (a) \(1.5\) moles (b) 1 mole (c) 4 moles (d) 2 moles

State whether the following statements are true or false. Gay-Lussac's law of combining volumes is applicable to the reaction, \(2 \mathrm{C}+\mathrm{O}_{2} \rightarrow 2 \mathrm{CO}_{2}\)
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