Question 1

Calculate the pressure exerted by 1.00 mol of a perfect gas that occupies a volume of 1.00 dm³ at a temperature of 25°C. A) 2.48 MPa B) 208 kPa C) 208 Pa D) 2.48 kPa

Accepted Answer

Using the ideal gas law, PV = nRT, where R = 8.314 J/(mol·K) and T = 298 K, the pressure P = (1 mol * 8.314 J/(mol·K) * 298 K) / (0.001 m³) = 2.48 MPa.

Question 2

The perfect gas model assumes that the average separation between the atoms or molecules is so great that they move independently of one another. Use the perfect gas equation to calculate the average volume per atom or molecule for a gas at a temperature of 298 K and a pressure of 1.00 bar. A) 41.1 $\mu$m³ B) 41.1 nm³ C) 41.1 Å³ D) 41.1 mm³

Accepted Answer

The perfect gas equation is PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature. To find the average volume per molecule, we use the equation in the form V/N = kT/P, where V/N is the volume per molecule, k is the Boltzmann constant, T is the temperature, and P is the pressure. Given T = 298 K and P = 1.00 bar (which is approximately equal to 100,000 Pa), and using the value of k = 1.38 x 10^-23 J/K, we can calculate the volume per molecule. The calculation yields a result in the order of 10^-23 m^3 per molecule, which, when converted to more practical units, gives a value in the order of tens of nm^3 (nanometers cubed) per molecule. Hence, the correct answer is in nanometers cubed, which corresponds to choice B.

Question 3

Use the kinetic theory of gases to determine the root-mean-square speed of phosphine, PH₃, molecules at a temperature of 450 °C. A) 570 m s^-1 B) 23 m s^-1 C) 730 m s^-1 D) 670 m s^-1

Accepted Answer

The root-mean-square speed ($v_{rms}$) of a gas molecule can be calculated using the formula $v_{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is the Boltzmann constant, $T$ is the temperature in Kelvin, and $m$ is the mass of a gas molecule in kilograms. To solve for $v_{rms}$ of phosphine ($PH_3$) at 450 °C, first convert the temperature to Kelvin (450 °C + 273.15 = 723.15 K) and calculate the molar mass of phosphine. The molar mass of phosphine is approximately 34 g/mol (1 phosphorus atom = 31 g/mol + 3 hydrogen atoms = 3 g/mol). Convert this mass to kilograms per mole (34 g/mol = 0.034 kg/mol) and then to kilograms per molecule by dividing by Avogadro's number ($6.022 \times 10^{23} \text{mol}^{-1}$). Plugging these values into the formula gives a $v_{rms}$ that closely matches the value provided in option C, indicating that it is the correct choice.

Question 4

Molecules from an equimolar mixture of gaseous silane, SiH₄, and helium, He, escape through effusion through a small hole in a cylinder. Calculate the rate of effusion of the silane molecules relative to the helium atoms. A) 2.82 B) 0.124 C) 0.353 D) 1.00

Accepted Answer

The rate of effusion is inversely proportional to the square root of the molar mass of the gas. The molar mass of SiH4 is 32.1 g/mol and that of He is 4.0 g/mol. The relative rate of effusion of SiH4 to He is √(4.0/32.1) = 0.353.

Question 5

Calculate the collision frequency in a gaseous sample of nitrogen molecules, N₂, at a temperature of 25 °C and pressure of 1 atm. The collision cross section of a nitrogen molecule is 0.43 nm² and the mean speed at this temperature is 474 m s^-1. A) 76000 s^-1 B) 907 * 10³ s^-1 C) 7.7*10⁹ s^-1 D) 1.0 * 10¹⁰ s^-1

Accepted Answer

The answer of Calculate the collision frequency in a gaseous...

Question 6

Calculate the mean free path between collisions for sulfur dioxide, SO₂, molecules at a pressure of 1 atm and a temperature of 25°C. The collision cross section for sulfur dioxide is 0.58 nm². A) 420 $\mu$m B) 500$\mu$m C) 50 nm D) 70 nm

Accepted Answer

The answer of Calculate the mean free path between collisions...

Question 7

The critical point of ammonia, NH₃, occurs at a pressure of 11.3 MPa, temperature of 406 K and molar volume of 72.5 cm³ mol^-1. Determine the compression factor of ammonia at the critical point. A) 0.243 B) 1 C) 4.12 D) 0.741

Accepted Answer

The critical point is the point at which the liquid and gas phases of a substance have the same density and are indistinguishable from each other. At the critical point, the compression factor is given by:Z = PV/RT = 1where P is the pressure, V is the molar volume, R is the gas constant, and T is the temperature.Substituting the given values into the equation, we get:Z = (11.3 MPa)(72.5 cm^3 mol^-1)/(8.314 J mol^-1 K^-1)(406 K) = 0.243Therefore, the compression factor of ammonia at the critical point is 0.243.

Question 8

For carbon dioxide, CO₂, the value of the second virial coefficient, B, is -142 cm³ mol^-1 at 273 K. Use the truncated form of the virial equation to calculate the pressure exerted by carbon dioxide gas at this temperature if the molar volume is 250 cm³ mol^-1. A) 14.2 MPa B) 3.92 MPa C) 9.08 MPa D) 4.28 MPa

Accepted Answer

The truncated virial equation is:$$P = \frac{RT}{V} + \frac{B}{V^2}$$Substituting the given values:$$P = \frac{(8.314 J mol^{-1} K^{-1})(273 K)}{250 cm^3 mol^{-1}} + \frac{(-142 cm^3 mol^{-1})}{(250 cm^3 mol^{-1})^2}$$$$P = 9.08 MPa$$

Question 9

Use the van der Waals equation of state to calculate the pressure exerted by exactly 1 mol of gaseous ethene, C₂H₂, held at a temperature of 425 K in a vessel of volume 1.25 dm³. The values of the van der Waals parameters for ethene are a = 4.552 atm dm⁶ mol^-2 and b = 5.82 * 10^-2 dm³ mol^-1. A) 2.83 MPa B) 2.67 MPa C) 2.97 MPa D) 291 kPa

Accepted Answer

The answer of Use the van der Waals equation of...

Question 10

The critical point of hydrogen sulifide, H₂S, occurs at a pressure of 9.01 MPa, volume of 97.9 m³ mol^-1 and temperature of 374 K. Calculate the values of the van der Waals parameters a and b. A) a = 12.7 MPa m⁶ mol^-2 and b = 12.5 m³ mol^-1 B) a = 89.2 MPa m⁶ mol^-2 and b = 32.6 m³ mol^-1 C) a = 36.2 MPa m⁶ mol^-2 and b = 92.9 m³ mol^-1 D) a = 57.1 MPa m⁶ mol^-2 and b = 90.1 m³ mol^-1

Accepted Answer

The answer of The critical point of hydrogen sulifide, H₂S,...

Quiz 1: The Propertiesof Gases

Calculate the pressure exerted by 1.00 mol of a perfect gas that occupies a volume of 1.00 dm3 at a temperature of 25°C.

The perfect gas model assumes that the average separation between the atoms or molecules is so great that they move independently of one another. Use the perfect gas equation to calculate the average volume per atom or molecule for a gas at a temperature of 298 K and a pressure of 1.00 bar.

Use the kinetic theory of gases to determine the root-mean-square speed of phosphine, PH3, molecules at a temperature of 450 °C.

Molecules from an equimolar mixture of gaseous silane, SiH4, and helium, He, escape through effusion through a small hole in a cylinder. Calculate the rate of effusion of the silane molecules relative to the helium atoms.

Calculate the collision frequency in a gaseous sample of nitrogen molecules, N2, at a temperature of 25 °C and pressure of 1 atm. The collision cross section of a nitrogen molecule is 0.43 nm2 and the mean speed at this temperature is 474 m s-1.

Calculate the mean free path between collisions for sulfur dioxide, SO2, molecules at a pressure of 1 atm and a temperature of 25°C. The collision cross section for sulfur dioxide is 0.58 nm2.

The critical point of ammonia, NH3, occurs at a pressure of 11.3 MPa, temperature of 406 K and molar volume of 72.5 cm3 mol-1. Determine the compression factor of ammonia at the critical point.

For carbon dioxide, CO2, the value of the second virial coefficient, B, is -142 cm3 mol-1 at 273 K. Use the truncated form of the virial equation to calculate the pressure exerted by carbon dioxide gas at this temperature if the molar volume is 250 cm3 mol-1.

Use the van der Waals equation of state to calculate the pressure exerted by exactly 1 mol of gaseous ethene, C2H2, held at a temperature of 425 K in a vessel of volume 1.25 dm3. The values of the van der Waals parameters for ethene are a = 4.552 atm dm6 mol-2 and b = 5.82 * 10-2 dm3 mol-1.

The critical point of hydrogen sulifide, H2S, occurs at a pressure of 9.01 MPa, volume of 97.9 m3 mol-1 and temperature of 374 K. Calculate the values of the van der Waals parameters a and b.

Calculate the pressure exerted by 1.00 mol of a perfect gas that occupies a volume of 1.00 dm³ at a temperature of 25°C.

Use the kinetic theory of gases to determine the root-mean-square speed of phosphine, PH₃, molecules at a temperature of 450 °C.

Molecules from an equimolar mixture of gaseous silane, SiH₄, and helium, He, escape through effusion through a small hole in a cylinder. Calculate the rate of effusion of the silane molecules relative to the helium atoms.

Calculate the collision frequency in a gaseous sample of nitrogen molecules, N₂, at a temperature of 25 °C and pressure of 1 atm. The collision cross section of a nitrogen molecule is 0.43 nm² and the mean speed at this temperature is 474 m s^-1.

Calculate the mean free path between collisions for sulfur dioxide, SO₂, molecules at a pressure of 1 atm and a temperature of 25°C. The collision cross section for sulfur dioxide is 0.58 nm².

The critical point of ammonia, NH₃, occurs at a pressure of 11.3 MPa, temperature of 406 K and molar volume of 72.5 cm³ mol^-1. Determine the compression factor of ammonia at the critical point.

For carbon dioxide, CO₂, the value of the second virial coefficient, B, is -142 cm³ mol^-1 at 273 K. Use the truncated form of the virial equation to calculate the pressure exerted by carbon dioxide gas at this temperature if the molar volume is 250 cm³ mol^-1.

The critical point of hydrogen sulifide, H₂S, occurs at a pressure of 9.01 MPa, volume of 97.9 m³ mol^-1 and temperature of 374 K. Calculate the values of the van der Waals parameters a and b.