/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 146 A large flask with a volume of \... [FREE SOLUTION] | 91影视

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Chapter 8: Problem 146

A large flask with a volume of \(936 \mathrm{mL}\) is evacuated and found to have a mass of \(134.66 \mathrm{g}\). It is then filled to a pressure of 0.967 atm at \(31^{\circ} \mathrm{C}\) with a gas of unknown molar mass and then reweighed to give a new mass of 135.87 g. What is the molar mass of this gas?

Short Answer

Expert verified
The molar mass of the gas is approximately \(32.97 \mathrm{g/mol}\).

Step by step solution

01

Convert the given values to appropriate units

We need to convert the given temperature from Celsius to Kelvin and the given volume from milliliters to liters: Temperature in Kelvin (K): T(K) = T(掳C) + 273.15 T(K) = 31 + 273.15 = 304.15 K Volume in liters (L): V(L) = V(mL) / 1000 V(L) = 936 / 1000 = 0.936 L
02

Find the mass of the gas inside the flask

Subtract the mass of the empty flask from the mass of the filled flask: Mass of gas = Mass of filled flask - Mass of empty flask Mass of gas = 135.87 g - 134.66 g = 1.21 g
03

Use the Ideal Gas Law to find the number of moles of gas

PV = nRT Solve for the number of moles (n): n = PV / RT We know the values of P, V, and T as well as the universal gas constant R (0.0821 L atm/mol K): n = (0.967 atm * 0.936 L) / (0.0821 L atm/mol K * 304.15 K) n = 0.0367 mol
04

Calculate the molar mass of the gas

Now that we have the number of moles and the mass of the gas, we can calculate the molar mass (M) using the following formula: M = mass (g) / moles M = 1.21 g / 0.0367 mol M = 32.97 g/mol The molar mass of the gas is approximately 32.97 g/mol.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding the Ideal Gas Law
The Ideal Gas Law provides a clear relationship between pressure (P), volume (V), temperature (T), and the number of moles (n) of a gas. Represented as the equation PV = nRT, this principle allows us to calculate one variable as long as the others are known.

When we reference the universal gas constant (R), which has a value of 0.0821 L atm/mol K, we are able to use the Ideal Gas Law across various units such as liters for volume, atmospheres for pressure, and kelvins for temperature. It's essential to ensure that all measurements comply with these units prior to applying the law, involving conversions such as moving from Celsius to Kelvin for temperature and milliliters to liters for volume.
Moles Calculation
The process of calculating moles, often represented as 'n' in chemical equations, is crucial in understanding the amounts of substances involved. In the context of the Ideal Gas Law, n can be isolated and calculated using the rearranged formula n = PV / RT. This step is fundamental in determining other properties such as molar mass.

The number of moles is a gateway to understanding the stoichiometry of chemical reactions, which is the quantitative relationship between reactants and products. Grasping moles calculation allows students to advance into more complex exercises, such as predicting the outcomes of chemical reactions or calculating the yields of products formed.
The Essence of Chemical Thermodynamics
Chemical Thermodynamics focuses on the study of energy changes during a chemical reaction. Crucial concepts include enthalpy, entropy, and Gibbs free energy. While this exercise deals with the molar mass of a gas, understanding the broader context of thermodynamics is valuable.

Thermodynamics helps explain why certain reactions occur spontaneously while others do not. It also underlines the importance of temperature as a factor influencing the behavior of gases, as seen in the necessity to convert Celsius to Kelvin while solving the provided exercise. Mastery of thermodynamics will ultimately enable students to predict the feasibility of chemical processes and comprehend the energy dynamics at play.

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Most popular questions from this chapter

At \(0^{\circ} \mathrm{C}\) a \(1.0\)-\(\mathrm{L}\) flask contains \(5.0 \times 10^{-2}\) mole of \(\mathrm{N}_{2}, 1.5 \times\) \(10^{2} \mathrm{mg} \mathrm{O}_{2},\) and \(5.0 \times 10^{21}\) molecules of \(\mathrm{NH}_{3} .\) What is the partial pressure of each gas, and what is the total pressurelin the flask?

Sulfur trioxide, \(\mathrm{SO}_{3},\) is produced in enormous quantities each year for use in the synthesis of sulfuric acid. $$\begin{aligned}\mathrm{S}(s)+\mathrm{O}_{2}(g) & \longrightarrow \mathrm{SO}_{2}(g) \\\2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{SO}_{3}(g)\end{aligned}$$ What volume of \(\mathrm{O}_{2}(g)\) at \(350 .^{\circ} \mathrm{C}\) and a pressure of \(5.25\) atm is needed to completely convert \(5.00 \mathrm{g}\) sulfur to sulfur trioxide?

Suppose two 200.0 - \(L\) tanks are to be filled separately with the gases helium and hydrogen. What mass of each gas is needed to produce a pressure of 2.70 atm in its respective tank at \(24^{\circ} \mathrm{C} ?\)

Consider separate \(1.0\) -\(\mathrm{L}\) samples of \(\mathrm{He}(g)\) and \(\mathrm{UF}_{6}(g),\) both at \(1.00\) atm and containing the same number of moles. What ratio of temperatures for the two samples would produce the same root mean square velocity?

Xenon and fluorine will react to form binary compounds when a mixture of these two gases is heated to \(400^{\circ} \mathrm{C}\) in a nickel reaction vessel. A \(100.0\) -\(\mathrm{mL}\) nickel container is filled with xenon and fluorine, giving partial pressures of \(1.24\) atm and \(10.10\) atm, respectively, at a temperature of \(25^{\circ} \mathrm{C}\). The reaction vessel is heated to \(400^{\circ} \mathrm{C}\) to cause a reaction to occur and then cooled to a temperature at which \(\mathrm{F}_{2}\) is a gas and the xenon fluoride compound produced is a nonvolatile solid. The remaining \(\mathrm{F}_{2}\) gas is transferred to another A \(100.0\) -\(\mathrm{mL}\) nickel container, where the pressure of \(\mathrm{F}_{2}\) at \(25^{\circ} \mathrm{C}\) is \(7.62\) atm. Assuming all of the xenon has reacted, what is the formula of the product?
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