/*! 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

A hot-air balloon is filled with air to a volume of \(4.00 \times\) \(10^{3} \mathrm{m}^{3}\) at \(745\) torr and \(21^{\circ} \mathrm{C}\). The air in the balloon is then heated to \(62^{\circ} \mathrm{C},\) causing the balloon to expand to a volume of \(4.20 \times 10^{3} \mathrm{m}^{3} .\) What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out. Thus the pressure in the balloon is always the same as that of the atmosphere.)

The total volume of hydrogen gas needed to fill the Hindenburg was \(2.0 \times 10^{8} \mathrm{L}\) at 1.0 atm and \(25^{\circ} \mathrm{C}\). Given that \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{H}_{2} \mathrm{O}(l)\) is \(-286 \mathrm{kJ} / \mathrm{mol},\) how much heat was evolved when the Hindenburg exploded, assuming all of the hydrogen reacted to form water?

At elevated temperatures, sodium chlorate decomposes to produce sodium chloride and oxygen gas. A \(0.8765\)-\(\mathrm{g}\) sample of impure sodium chlorate was heated until the production of oxygen gas ceased. The oxygen gas collected over water occupied \(57.2 \mathrm{mL}\) at a temperature of \(22^{\circ} \mathrm{C}\) and a pressure of \(734\) torr. Calculate the mass percent of \(\mathrm{NaClO}_{3}\) in the original sample. (At \(22^{\circ} \mathrm{C}\) the vapor pressure of water is \(19.8\) torr.)

Consider an equimolar mixture (equal number of moles) of two diatomic gases \(\left(A_{2} \text { and } B_{2}\right)\) in a container fitted with a piston. The gases react to form one product (which is also a gas) with the formula \(A_{x} B_{y}\). The density of the sample after the reaction is complete (and the temperature returns to its original state) is \(1.50\) times greater than the density of the reactant mixture. a. Specify the formula of the product, and explain if more than one answer is possible based on the given data. b. Can you determine the molecular formula of the product with the information given or only the empirical formula?

Consider two gases, \(A\) and \(B\), each in a \(1.0\) -\(\mathrm{L}\) container with both gases at the same temperature and pressure. The mass of gas \(A\) in the container is \(0.34\) \(\mathrm{g}\) and the mass of gas \(B\) in the container is \(0.48 \mathrm{g}\). a. Which gas sample has the most molecules present? Explain. b. Which gas sample has the largest average kinetic energy? Explain. c. Which gas sample has the fastest average velocity? Explain. d. How can the pressure in the two containers be equal to each other since the larger gas \(B\) molecules collide with the container walls more forcefully?
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