Molar Mass the Mole and Molar Volume Conversion Review

Learning Objectives

1. Convert from mass or moles of one substance to mass or moles of another substance in a chemic reaction.

We have established that a balanced chemical equation is balanced in terms of moles too equally atoms or molecules. Nosotros have used counterbalanced equations to set up ratios, now in terms of moles of materials, that we can use as conversion factors to answer stoichiometric questions, such as how many moles of substance A react with so many moles of reactant B. We can extend this technique even further. Recall that nosotros can relate a tooth amount to a mass amount using molar mass. Nosotros can use that power to respond stoichiometry questions in terms of the masses of a particular substance, in improver to moles. We do this using the post-obit sequence:

Collectively, these conversions are chosen mole-mass calculations .

As an example, consider the counterbalanced chemical equation

Fe₂O_three + 3SO₃ → Fe_two(SO_iv)₃

If we have 3.59 mol of Iron₂O₃, how many grams of SO₃ can react with it? Using the mole-mass calculation sequence, we can determine the required mass of SO_three in two steps. First, we construct the appropriate molar ratio, determined from the balanced chemic equation, to calculate the number of moles of SO₃ needed. Then using the molar mass of SO₃ as a conversion cistron, nosotros determine the mass that this number of moles of SO_iii has.

The showtime stride resembles the exercises nosotros did in Department 6.4 "Mole-Mole Relationships in Chemic Reactions". Every bit usual, we offset with the quantity we were given:

[latex]three.59\cancel{\text{ mol Fe}_2\text{O}_3}\times\frac{three\text{ mol SO}_3}{1\cancel{\text{ mol Fe}_2\text{O}_3}}[/latex] = 10.8 mol SO₃

The mol Fe₂O_three units abolish, leaving mol SO_iii unit of measurement, and based on 3 sig figs in the 3.59 mol SO₃, the answer was rounded to 3 sig figs.  As y'all will encounter soon, such intermediate rounding introduces rounding error in the terminal reply.

Next convert this answer to grams of SO₃, using the molar mass of Then₃ as the conversion cistron.

[latex]10.8\cancel{\text{ mol SO}_3}\times\frac{fourscore.06\text{ chiliad And then}_3}{1\cancel{\text{ mol And so}_3}}[/latex] = 865 g SO₃

The answer to this step is expressed to three significant figures. Thus, in a two-step process, we find that 865 g of SO₃ will react with 3.59 mol of Iron₂O₃. Many problems of this blazon can be answered in this way.

To avert rounding error, information technology is better to do multi-pace problems all at once, keeping intermediate answers in the figurer and rounding only once at the end.:

Notice that, when rounding after each step, the respond was 865 g SO_three.  But when the calculator was used to hold onto all of the decimal places of the intermediate number, the respond came out to 862 g So₃.  This should phone call to heed the fact that the concluding digit of a measured number or of a calculated number based on measurements is an uncertain estimate.  Even so, the nearly accurate answer is the one obtained past doing all of the steps at once and rounding for the correct number of sig figs at the very finish.  In this instance the most authentic reply is 862 g Then_three.

Example viii

How many grams of CO₂ are produced if 2.09 mol of HCl are reacted according to this balanced chemical equation?

CaCO_iii + 2HCl → CaCl₂ + CO_two + H₂O

Solution

Our strategy will be to convert from moles of HCl to moles of CO₂ and then from moles of CO₂ to grams of CO_two. We will need the molar mass of CO₂, which is 44.01 g/mol. Performing these two conversions in a single-line gives 46.0 yard of CO₂:

The molar ratio betwixt CO₂ and HCl comes from the balanced chemical equation.

Skill-Building Exercise

1. How many grams of glucose (C_viH₁₂O_six) are produced if 17.3 mol of H₂O are reacted according to this balanced chemic equation?

   6CO₂ + 6H₂O → C₆H₁₂O_{half dozen} + 6O_two

It is a small stride from mole-mass calculations to mass-mass calculations . If we start with a known mass of one substance in a chemical reaction (instead of a known number of moles), we can calculate the corresponding masses of other substances in the reaction. The first step in this case is to convert the known mass into moles, using the substance's molar mass as the conversion gene. And so—and only then—nosotros utilise the balanced chemical equation to construct a conversion factor to convert that quantity to moles of another substance, which in plough tin be converted to a corresponding mass. Sequentially, the procedure is as follows:

This three-part procedure should be combined into a single calculation that contains iii conversion factors every bit shown in the post-obit example.

Example 9

Methyl hydride can react with elemental chlorine to make carbon tetrachloride (CCl₄). The balanced chemical equation is as follows:

CH_four + 4Cl_ii → CCl₄ + 4HCl

How many grams of HCl are produced by the reaction of 100.0 thousand of CH_iv?

Solution

The kickoff conversion factor converts the mass of CH_iv to moles of CH₄, using the molar mass of CH_four (16.05 thousand/mol).  Since the unit of measurement "one thousand CH_four"  must cancel, the molar mass is inverted to create the starting time conversion factor:

[latex]\frac{1\text{ mol CH}_4}{sixteen.05\text{ k CH}_4}[/latex]

The second conversion must bridge from mol CH₄ to mol HCl.   The coefficients in the balanced chemical equation represent the ratio of moles HCl and moles CH_4, with mol CH_four in the denominator so information technology will cancel:

[latex]\frac{4\text{ mol HCl}}{i\text{ mol CH}_4}[/latex]

The third and terminal conversion factor uses the molar mass of HCl (36.46 g/mol) , this fourth dimension without inversion because mol HCl must be cancelled:

[latex]\frac{36.46\text{ g HCl}}{1\text{ mol HCl}}[/latex]

Combining the three conversion factors into a single, multi-stride problem:

[latex]100.0\abolish{\text{ g CH}_4}\times{\frac{ane\text{ mol CH}_4}{16.05\cancel{\text{ g CH}_4}}}\times{\frac{4\text{ mol HCl}}{1\cancel{\text{ mol CH}_4}}}\times{\frac{36.46\text{ 1000 HCl}}{1\abolish{\text{ mol HCl}}}}[/latex] = 908.7 g HCl

In that location were 4 sig figs in the measured number 100.0 g CH₄ and the molar masses each had 4 sig figs too.  The whole numbers from the equation coefficients are verbal numbers and do not limit the sig figs.  Therefore, the final answer is rounded to have four sig figs.

Skill-Building Exercise

1. The oxidation of propanal (CH₃CH₂CHO) to propionic acid (CH₃CH₂COOH) has the following balanced chemic equation:

   3CH₃CH_iiCHO + One thousand₂Cr₂O_seven +4H₂And so_iv → 3CH_threeCH₂COOH + Cr_two(SO₄)₃ + 4H₂O + Grand_twoSo₄
   

   How many grams of propionic acid are produced past the reaction of 135.viii g of K_iiCr_iiO₇?

Concept Review Exercises

1. What is the general sequence of conversions for a mole-mass calculation?

2. What is the full general sequence of conversions for a mass-mass calculation?

Answers

To Your Health: The Synthesis of Taxol

Taxol is a powerful anticancer drug that was originally extracted from the Pacific yew tree (Taxus brevifolia). Every bit you tin can see from the accompanying figure, taxol is a very complicated molecule, with a molecular formula of C₄₇H₅₁NO₁₄. Isolating taxol from its natural source presents certain challenges, mainly that the Pacific yew is a slow-growing tree, and the equivalent of six trees must be harvested to provide enough taxol to treat a single patient. Although related species of yew copse also produce taxol in small amounts, at that place is significant involvement in synthesizing this circuitous molecule in the laboratory.

Subsequently a 20-year effort, ii research groups appear the complete laboratory synthesis of taxol in 1994. However, each synthesis required over 30 divide chemic reactions, with an overall efficiency of less than 0.05%. To put this in perspective, to obtain a single 300 mg dose of taxol, yous would have to begin with 600 m of starting textile. To treat the 26,000 women who are diagnosed with ovarian cancer each year with one dose, almost 16,000 kg (over 17 tons) of starting fabric must be converted to taxol. Taxol is also used to treat breast cancer, with which 200,000 women in the United States are diagnosed every year. This just increases the amount of starting material needed.

Clearly, there is intense interest in increasing the overall efficiency of the taxol synthesis. An improved synthesis non only volition be easier just besides volition produce less waste materials, which will allow more than people to accept advantage of this potentially life-saving drug.

Figure six.4 The Structure of the Cancer Drug Taxol. Because of the complexity of the molecule, hydrogen atoms are not shown, but they are nowadays on every atom to give the atom the correct number of covalent bonds (4 bonds for each carbon atom).

Fundamental Takeaway

• A balanced chemical equation can be used to relate masses or moles of different substances in a reaction.

Exercises

1. Given the post-obit unbalanced chemic equation,

   H₃PO₄ + NaOH → H_iiO + Na₃PO₄

   what mass of H₂O is produced past the reaction of 2.35 mol of H₃PO₄?

2. Given the following unbalanced chemical equation,

   C_twoH₆ + Br₂ → C₂H₄Br₂ + HBr

   what mass of HBr is produced if 0.884 mol of C₂H₆ is reacted?

3. Certain fats are used to make lather, the outset step existence to react the fat with water to make glycerol (likewise known as glycerin) and compounds chosen fatty acids. One instance is as follows:

   C₃H₅(OOC(CH₂)₁₄ CH_three)₃ (a fat)+ 3H₂O → C₃H₅(OH)_three (glycerol)+3CH₃(CH ₂)₁₄COOH (fat acid)

   How many moles of glycerol tin be made from the reaction of 1,000.0 k of C₃H₅(OOC(CH_two)_fourteenCH₃)_iii?

4. Photosynthesis in plants leads to the general overall reaction for producing glucose (C₆H₁₂O₆):

   6CO₂ + 6H₂O → C_viH₁₂O₆ + 6O₂

   How many moles of glucose can be made from the reaction of 544 chiliad of CO_two?

5. Atmospheric precipitation reactions, in which a solid (called a precipitate) is a production, are commonly used to remove sure ions from solution. The balanced equation for i such reaction is every bit follows:

   Ba(NO_iii)₂(aq) + Na₂SO₄(aq) → BaSO₄(s) + 2NaNO₃(aq)

   How many grams of Na₂And so_four are needed to precipitate all the barium ions produced by 43.9 g of Ba(NO_iii)₂?

6. Nitroglycerin [C₃H_five(ONO₂)₃] is made by reacting nitric acid (HNO₃) with glycerol [C₃H_v(OH)₃] according to this counterbalanced equation:

   C_iiiH_v(OH)_three + 3HNO₃ → C_iiiH_v(ONO₂)₃ + 3H₂O

   If 87.4 one thousand of HNO₃ are reacted with excess glycerol, what mass of nitroglycerin tin can be made?

7. Antacids are bases that neutralize acids in the digestive tract. Magnesium hydroxide [Mg(OH)₂] is one such antacid. It reacts with hydrochloric acid in the stomach according to the following counterbalanced equation:

   Mg(OH)₂ + 2HCl → MgCl_ii + 2H_iiO

   How many grams of HCl tin a 200. mg dose of Mg(OH)_two neutralize?

8. Acid rain is acquired by the reaction of nonmetal oxides with water in the atmosphere. One such reaction involves nitrogen dioxide (NO_two) and produces nitric acid (HNO_three):

   3NO₂ + H₂O → 2HNO₃ + NO

   If ane.82 × 10^xiii g of NO₂ enter the atmosphere every year due to human activities, potentially how many grams of HNO₃ can exist produced annually?

9. A simplified version of the processing of fe ore into atomic number 26 metal is as follows:

   2Fe₂O₃ + 3C → 4Fe + 3CO_ii

   How many grams of C are needed to produce i.00 × ten⁹ g of Iron?

10. The SS Hindenburg independent near five.33 × x⁵ g of H₂ gas when it burned at Lakehurst, New Jersey, in 1937. The chemical reaction is as follows:

    2H_two + O₂ → 2H₂O

    How many grams of H₂O were produced?

Answers

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Source: https://courses.lumenlearning.com/suny-monroecc-orgbiochemistry/chapter/6-5-mole-mass-and-mass-mass-problems/

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