Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 9: Problem 166

Consider the balanced chemical equation \(2 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{C}+\mathrm{D}\) When \(8.0 \mathrm{~g}\) of A reacts completely with \(6.0 \mathrm{~g}\) of \(\mathrm{B}\), \(10.0 \mathrm{~g}\) of \(\mathrm{C}\) and \(4.0 \mathrm{~g}\) of \(\mathrm{D}\) are produced. Assuming the yield is \(100 \%\), (a) Which has a greater molar mass, A or C? (b) Which has a greater molar mass, A or B? (c) Which has a greater molar mass, A or D? (d) If the molar mass of \(\mathrm{A}\) is \(24.0 \mathrm{~g} / \mathrm{mol}\), determine the molar mass of \(\mathrm{B}, \mathrm{C}\), and \(\mathrm{D}\).

Short Answer

Expert verified
(a) C has a greater molar mass than A. (b) B has a greater molar mass than A. (c) A and D have equal molar masses. (d) The molar masses of B, C, and D are 36.0 g/mol, 30.0 g/mol, and 24.0 g/mol, respectively.

Step by step solution

01

Calculate mole ratios A and B

To calculate the mole ratio between reactants A and B, we need to divide the mass of each reactant by its respective molar mass (we will denote these molar mass as M_A, M_B, M_C, and M_D for the four substances, respectively). Since we know the molar mass of A, we can calculate the number of moles of A. Then, we can determine the ratio of moles of A to moles of B using the balanced chemical equation. n_A = \(\frac{mass_A}{M_A}\) = \(\frac{8.0~g}{24.0~g/mol}\) = \(0.333~mol\) Since the balanced chemical equation states there is a 2-to-1 ratio for A to B, we can determine the number of moles of B: n_B = \(\frac{1}{2}\)n_A = \(\frac{1}{2}\)(0.333 mol) = \(0.167~mol\)
02

Calculate the molar mass of B

Now that we know the number of moles of B, we can calculate the molar mass using the mass of B. M_B = \(\frac{mass_B}{n_B}\) = \(\frac{6.0~g}{0.167~mol}\) = \(36.0~g/mol\)
03

Determine which has a greater molar mass: A or B

Since the molar mass of A is 24.0 g/mol and the molar mass of B is 36.0 g/mol, B has a greater molar mass than A.
04

Calculate the number of moles of C and D

Using the balanced chemical equation, we see that the mole ratio of A:C is 2:2 = 1:1 and A:D is 2:1. Therefore, the number of moles of C must be equal to the number of moles of A, and the number of moles of D must be equal to half the number of moles of A: n_C = n_A = \(0.333~mol\) n_D = \(\frac{1}{2}\)n_A = \(0.167~mol\)
05

Calculate the molar mass of C and D

We can calculate the molar masses of C and D using their masses and the calculated number of moles. M_C = \(\frac{mass_C}{n_C}\) = \(\frac{10.0~g}{0.333~mol}\) = \(30.0~g/mol\) M_D = \(\frac{mass_D}{n_D}\) = \(\frac{4.0~g}{0.167~mol}\) = \(24.0~g/mol\)
06

Determine which has a greater molar mass: A, C, and D

Comparing the molar masses of A, C and D: - Molar mass of A: 24.0 g/mol - Molar mass of C: 30.0 g/mol - Molar mass of D: 24.0 g/mol So, C has a greater molar mass than A, and A and D have equal molar masses. The answers to the given questions are: (a) C has a greater molar mass than A. (b) B has a greater molar mass than A. (c) A and D have equal molar masses. (d) The molar masses of B, C, and D are 36.0 g/mol, 30.0 g/mol, and 24.0 g/mol, respectively.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Caffeine is made up of \(49.48 \%\) by mass \(C, 5.19 \%\) by mass \(\mathrm{H}, 28.85 \%\) by mass \(\mathrm{N}\), and \(16.48 \%\) by mass \(\mathrm{O}\). If its molar mass is approximately \(194 \mathrm{~g} / \mathrm{mol}\), what is the molecular formula of caffeine?

How many grams of sulfur hexafluoride would you need to have \(5.25 \times 10^{24}\) fluorine atoms?

Consider the unbalanced chemical equation \(\mathrm{As}_{4} \mathrm{~S}_{6}+\mathrm{O}_{2} \rightarrow \mathrm{As}_{4} \mathrm{O}_{6}+\mathrm{SO}_{2}\) (a) How many grams of \(\mathrm{O}_{2}\) are needed to react completely with \(58.9 \mathrm{~g}\) of \(\mathrm{As}_{4} \mathrm{~S}_{6}\) ? (b) If \(41.2 \mathrm{~g}\) of \(\mathrm{SO}_{2}\) is produced, what is the percent yield for the reaction?

Determine the mass percent of each element in aluminum sulfate.

Some calcium supplements contain calcium citrate, \(\mathrm{Ca}_{3}\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{O}_{7}\right)_{2}\), and others contain calcium carbonate, \(\mathrm{CaCO}_{3}\). Which compound has the higher mass percent of calcium?
See all solutions

Recommended explanations on Chemistry Textbooks

Organic Chemistry

Read Explanation

Nuclear Chemistry

Read Explanation

Physical Chemistry

Read Explanation

The Earths Atmosphere

Read Explanation

Chemical Analysis

Read Explanation

Ionic and Molecular Compounds

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free