Assume that helium behaves as an ideal gas. What is the estimated density of 1.0 g of helium gas at a temperature of 27 °C and a pressure of 3.0 atm? (Note: Use R = 0.0821 L∙atm∙mol⁻¹∙K⁻¹)

Question

Quizplus · Accepted Answer

11ecba2d_1237_95c5_a3bf_61fb7aa51792_MD0008_00 An ideal gas is a hypothetical gas with well-behaved (idealized) characteristics used to make a simplified model to predict the behavior of real gases. Following this model, the behavior of a gas can be described by the ideal gas law: 11ecba2d_1237_95c6_a3bf_d5a3baa05ece_MD0008_00 where P is the pressure, V is the volume occupied, n is the number of moles, T is the absolute temperature (in Kelvin), and R is a constant. If both the mass of a gas sample and the volume that it occupies are known, the gas density ρ can be evaluated as the mass m per unit volume V: 11ecba2d_1237_95c7_a3bf_516d0516b90a_MD0008_00 In this question, the volume occupied by the helium gas sample under the given conditions must be calculated before the density can be estimated. Use of the ideal gas law requires that the mass of the 1.0-g sample of helium gas be converted into moles using the molar mass of helium: 11ecba2d_1237_95c8_a3bf_d71ae628ea5f_MD0008_00 After conversion of the temperature from Celsius to Kelvin (27 °C + 273 = 300 K) and application of the ideal gas law (with R rounded for estimation), the volume occupied by the helium gas is: 11ecba2d_1237_95c9_a3bf_d9afb156412b_MD0008_00 Dividing the mass of the gas by the calculated volume (expressed in milliliters) gives an estimated density of: 11ecba2d_1237_bcda_a3bf_af8626d3ba53_MD0008_00 (Choice A) 1.3 × 10⁻⁴ is obtained either by not converting the grams of helium to moles of helium when calculating the gas volume or by dividing the moles of helium, rather than the mass of helium, by the correctly calculated gas volume. (Choice C) 1.0 × 10⁻³ is calculated by incorrectly using a molar mass of 8.00 g/mol. Like all noble gases, He has a full valence shell and exists as a monatomic gas in its elemental state. Because the valence shell of He (ie, a 2s orbital) has a maximum capacity of 2 electrons, He does not form bonds with other atoms. As such, diatomic He₂(g) does not form and helium is not one of the common diatomic elements. (Choice D) The mass of gas must be converted into moles and the temperature must be converted from Celsius to Kelvin when using the ideal gas law. Educational objective: An ideal gas is a hypothetical gas with well-behaved (idealized) characteristics used to make a simplified model to predict the behavior of real gases. The behavior of a gas can be described by the ideal gas law. Using a calculated gas volume and its mass, the gas density (mass per unit volume) can be evaluated.

Assume That Helium Behaves as an Ideal Gas