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Chapter 6: Problem 40

A 132.10 mL glass vessel weighs 56.1035 g when evacuated and \(56.2445 \mathrm{g}\) when filled with the gaseous hydrocarbon acetylene at \(749.3 \mathrm{mmHg}\) and \(20.02^{\circ} \mathrm{C}\) What is the molar mass of acetylene? What conclusion can you draw about its molecular formula?

Short Answer

Expert verified
The molar mass of acetylene is approximately 26.1 g/mol, which indicates that its molecular formula is \(C_2H_2\).

Step by step solution

01

Calculate Mass of Gas

First, calculate the mass of the gas in the container by subtracting the weight of the evacuated container from the weight of the container filled with acetylene: Mass (gas) = \(56.2445g - 56.1035g = 0.1410g\).
02

Convert Units

Convert pressure from mmHg to atm: \[Pressure (P) = \frac{749.3mmHg}{760 mmHg/atm} = 0.9859 atm\]. Convert temperature from Celsius to Kelvin: \[Temperature (T) = 20.02° C + 273.15 = 293.17 K\].
03

Calculate Moles

Use the Ideal Gas Law formula to calculate the number of moles (n). Rearrange the formula to calculate n as follows: n = PV/RT. \[n (acetylene) = \frac{(0.9859 atm)(0.13210 L)}{(0.0821 L.atm/mol.K)(293.17 K)} = 0.0054 mol\]
04

Calculate Molar Mass

Next, find the molar mass by dividing the mass by the number of moles. \[Molar mass = \frac{0.1410g}{0.0054 mol} = 26.1 g/mol \]
05

Determine Molecular Formula

The molecular formula of a compound is determined by the molar mass. The molar mass of acetylene (\(C_2H_2\)) is approximately 26 g/mol, so the empirical formula must be \(C_2H_2\)

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Most popular questions from this chapter

The gas with the greatest density at STP is (a) \(\mathrm{N}_{2} \mathrm{O}\) (b) \(\mathrm{Kr} ;\) (c) \(\mathrm{SO}_{3} ;\) (d) \(\mathrm{Cl}_{2}\).

Hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2},\) is used to disinfect contact lenses. How many milliliters of \(\mathrm{O}_{2}(\mathrm{g})\) at \(22^{\circ} \mathrm{C}\) and \(752 \mathrm{mmHg}\) can be liberated from \(10.0 \mathrm{mL}\) of an aqueous solution containing \(3.00 \% \mathrm{H}_{2} \mathrm{O}_{2}\) by mass? The density of the aqueous solution of \(\mathrm{H}_{2} \mathrm{O}_{2}\) is \(1.01 \mathrm{g} / \mathrm{mL}\) $$2 \mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)+\mathrm{O}_{2}(\mathrm{g})$$

A 1.65 g sample of \(\mathrm{Al}\) reacts with excess \(\mathrm{HCl}\), and the liberated \(\mathrm{H}_{2}\) is collected over water at \(25^{\circ} \mathrm{C}\) at a barometric pressure of \(744 \mathrm{mmHg} .\) What volume of gaseous mixture, in liters, is collected? $$2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})$$

How many liters of \(\mathrm{H}_{2}(\mathrm{g})\) at STP are produced per gram of \(\mathrm{Al}(\mathrm{s})\) consumed in the following reaction? \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\)

In the reaction of \(\mathrm{CO}_{2}(\mathrm{g})\) and solid sodium peroxide \(\left(\mathrm{Na}_{2} \mathrm{O}_{2}\right),\) solid sodium carbonate \(\left(\mathrm{Na}_{2} \mathrm{CO}_{3}\right)\) and oxy- gen gas are formed. This reaction is used in submarines and space vehicles to remove expired \(\mathrm{CO}_{2}(\mathrm{g})\) and to generate some of the \(\mathrm{O}_{2}(\mathrm{g})\) required for breathing. Assume that the volume of gases exchanged in the lungs equals \(4.0 \mathrm{L} / \mathrm{min},\) the \(\mathrm{CO}_{2}\) content of expired air is \(3.8 \% \mathrm{CO}_{2}\) by volume, and the gases are at \(25^{\circ} \mathrm{C}\) and \(735 \mathrm{mmHg}\). If the \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) in the above reaction are measured at the same temperature and pressure, (a) how many milliliters of \(\mathrm{O}_{2}(\mathrm{g})\) are produced per minute and \((\mathrm{b})\) at what rate is the \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) consumed, in grams per hour?
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