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Chapter 6: Problem 27

What is the volume, in milliliters, occupied by \(89.2 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g})\) at \(37^{\circ} \mathrm{C}\) and \(737 \mathrm{mmHg} ?\)

Short Answer

Expert verified
By proceeding through these 5 steps, we obtain the volume of CO2 in liters. To get the volume in milliliters, multiply by 1000. Don't forget to use significant figures.

Step by step solution

01

Finding Molar Mass of CO2

First, we need to find out the molar mass of CO2. Carbon (C) has a molar mass of 12.01 g/mol and Oxygen (O) has a molar mass of 16.00 g/mol. Given that CO2 has 1 Carbon atom and 2 Oxygen atoms, we can compute the molar mass as follows: \[ MolarMass_{CO2} = 12.01\ g/mol + 2 * 16.00\ g/mol = 44.01\ g/mol \]
02

Converting grams to moles

Next, we convert the mass of CO2 in grams to moles. We need to divide the given mass by the molar mass: \[n =\frac{89.2\ g\ CO2}{44.01\ g/mol} \]
03

Converting Temperature to Kelvin

The ideal gas law requires the temperature to be in Kelvin. To convert from Celsius to Kelvin, we add 273.15: \[ T = 37^{\circ}C + 273.15 = 310.15\ K \]
04

Converting pressure to atm

The pressure needs to be in atmospheres (atm) for the ideal gas law. To convert from mmHg to atm, we use the conversion factor 1 atm = 760 mmHg: \[ P = \frac{737\ mmHg}{760\ mmHg/atm} \]
05

Substitute and Solve

We have the following values ready: number of moles (n), temperature (T), pressure (P), and ideal gas constant (R=0.0821 L.atm/mol.K). Now, inserting these values into the ideal gas law equation PV=nRT, we solve for V: \[ V = \frac{nRT}{P} \]

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Most popular questions from this chapter

Explain why it is necessary to include the density of \(\mathrm{Hg}(1)\) and the value of the acceleration due to gravity, \(g,\) in a precise definition of a millimeter of mercury (page 194 ).

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) has a volume of \(26.7 \mathrm{L}\) at 762 Torr. What is the new volume if, with the temperature and amount of gas held constant, the pressure is (a) lowered to 385 Torr; (b) increased to 3.68 atm?

Monochloroethylene is used to make polyvinylchloride (PVC). It has a density of \(2.56 \mathrm{g} / \mathrm{L}\) at \(22.8^{\circ} \mathrm{C}\) and 756 mmHg. What is the molar mass of monochloroethylene? What is the molar volume under these conditions?

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(24^{\circ} \mathrm{C}\) The volume of gas is 1.16 L. In a subsequent experiment, it is determined that the mass of \(\mathrm{O}_{2}\) present is 1.46 g. What must have been the barometric pressure at the time the gas was collected? (Vapor pressure of water \(=22.4 \text { Torr. })\)

The Haber process is the principal method for fixing nitrogen (converting \(\mathrm{N}_{2}\) to nitrogen compounds). $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$$ Assume that the reactant gases are completely converted to \(\mathrm{NH}_{3}(\mathrm{g})\) and that the gases behave ideally. (a) What volume of \(\mathrm{NH}_{3}(\mathrm{g})\) can be produced from 152 \(\mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L}\) of \(\mathrm{H}_{2}(\mathrm{g})\) if the gases are measured at \(315^{\circ} \mathrm{C}\) and 5.25 atm? (b) What volume of \(\mathrm{NH}_{3}(\mathrm{g}),\) measured at \(25^{\circ} \mathrm{C}\) and\(727 \mathrm{mmHg},\) can be produced from \(152 \mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L} \mathrm{H}_{2}(\mathrm{g}),\) measured at \(315^{\circ} \mathrm{C}\) and \(5.25 \mathrm{atm} ?\)
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