How much sulfur dioxide is produced by the reaction of l.0Og S and all the oxygen in the atmosphere of the earth?

Stoichiometry

13. Since the balanced equation was given in the statement of the problem, the problem is as easy to solve as the previous ones

8.39. How much sulfur dioxide is produced by the reaction of l.0Og S and all the oxygen in the atmosphere of the earth?

Ans. In this problem, it is obvious that the oxygen in the entire earth's atmosphere is in excess, so that no preliminary calculation need be done.

s +

^0,

- ^so,

1 rnol SO, rnol S

64.1 g SO, 0.0312mol S(

)

⁼ 0.0312mol SO,

8.40. How can you recognize a limiting quantities problem?

Ans. The quantities of two reactants (or products) are given in the problem. They might be stated in any terms-moles, mass, etc.-but they must be given for the problem to be a limiting quantities problem.

144

8.41.

8.42.

8.43.

8.44.

p rob1 e m?

Ans. ( a )

( b )

STOICHIOMETRY [CHAP. 8

( a ) How many moles of C1, will react with 7.0mol Na to produce NaCl? ( b ) If 5.0mol C1, is treated with 7.0mol Na, how much C1, will react? ( c ) What is the limiting quantity in this

2Na+C12-2NaCl 1 rnol Cl,

7.0mol Na

(

^{2mol Na}

j

⁼ 3.5 mol CI, reacts

We calculated in part ( a ) that 3.5mol of CI, is needed to react. As long as we have at least 3.5mol present, 3.5mol C1, will react. (c.) Since we have more Cl, than that, the Na is in limiting quantity.

If you were treating two chemicals, one cheap and one expensive, to produce a product, which one would you use in excess, if one of them had to be in excess?

Ans. Economically, it would be advisable to use the cheap one in excess, since more product could be obtained per dollar by using up all the expensive reactant.

( U ) The price of pistachio nuts is $5.00 per pound. If a grocer has 13pounds for sale, and a

buyer has $24.00 to buy nuts with, what is the maximum number of pounds that can be sold?

( b ) Consider the reaction

KMnO,

+

^5FeC1,

+

^{8HCl+ MnCl,}

+

^SFeCl,

+

^{4 H 2 0}

+

KCl

If 24.0mol of FeCl, and 13.0mol of KMnO, are mixed with excess HCl, how many moles of MnCl, can be formed?

With $24, the buyer can buy

Since the seller has more nuts than that, the money is in limiting quantity, and controls the amount of the sale.

With 24.0 rnol FeCl,,

= 4.80 rnol KMnO, required 1 rnol KMnO,

5 rnol FeCl, 24 .O rnol FeCl

,

Since the number of moles of KMnO, present (13.0mol) exceeds that number, the limiting quantity is the number of moles of FeCl,.

= 4.80 rnol MnCI, 1 rnol MnCl,

5 rnol FeCI, 24.0 rnol FeCl

In each of the following cases, determine which reactant is present in excess, and tell how many moles in excess it is.

Equation Moles Present

(

4

( b ) P,O,,,

+

6 H 2 0 ---4H,PO, 0.50mol P,OI,,, 3.0mol H,O ( c )

( d )

( 4

2Na

+

C1,

---

^2NaCl 7.9 mol Na, 3.0 mol C1 HNO,

+

^{NaOH -+ NaNO,}

+

^H,O

Ca(HCO,),

+

^{2 HCl}

---

^CaC1,

⁺

^{2 CO,}

⁺

^{2 H,O}

H,PO,

+

3 NaOH

---

^Na,PO,

⁺

^{3 H,O} 2.0 mol acid, 2.1 mol base 3.5 mol HCI, 1 mol Ca(HCO,),

0.13 rnol acid, 1.05 mol NaOH 2mol Na

Ans. ((0 3.0mol Cl,

[

^{_____ mol}

^cl, )

^{= 6.0} rnol Na required

CHAP. 81 STOICHIOMETRY 145

There is 1.9mol more Na present than is required.

6mol H,O

( b ) 0.50mol P,O1,,

(

mol p,o,,,

)

⁼ 3.0mol H,O required

Neither reagent is in excess; there is just enough H,O to react with all the P,O,(,.

= 2.1 rnol HNO, required 1 rnol HNO,

rnol NaOH ( c ) 2.1 rnol NaOH

There is not enough HNO, present; NaOH is in cxccss.

1 rnol NaOH

2.0mol HNO,

[

^{mol HNO,}

)

⁼ 2.0mol NaOH required There is 0.1 rnol NaOH in excess.

= 2.0mol HCI required 2mol HCI

i

rnol Ca( HCO,), ( d ) 1.0mol Ca(HCO,),

There is 1.5 rnol HCI in excess.

3 rnol NaOH

rnol H

,

^{PO, =} 0.39 rnol NaOH required ( e ) 0.13mol H,PO,

There is 1.05 - 0.39 = 0.66mol NaOH in excess.

8.45. For the following reaction,

2NaOH

+

^{H,SO, --+ Na,SO,}

+

2H,O

How many moles of NaOH would react with 0.750mol H,SO,? How many moles of Na,SO, would be produced?

If 0.750mol of H,SO, and 2.00mol NaOH were mixed, how much NaOH would react?

If 73.5 g H,SO, and 80.0g NaOH were mixed, how many grams of Na,SO, would be produced?

= 1 S O rnol NaOH 2mol NaOH

rnol H,SO, 0.750 rnol H,SO,

= 0.750mol Na,SO, 1 rnol Na,SO,

i

^{rnol H ?SO,}

0.750 rnol H,SO,

1.50mol NaOH, as calculated in part ( a ) .

This is really the same problem as part (h), except that it is stated in grams, because 73.5g H,SO, is 0.750mol and 8O.Og NaOH is 2.00mol NaOH.

= 106g Na,SO, 142g Na,SO,

rnol Na,SO, 0.750 rnol Na2S0,

8.46. For the reaction

3 HCl

+

Na,PO, --+ H,PO,

+

^{3 NaCl}

a chemist added 3.9mol of HCl and a certain quantity of Na,PO, to a reaction vessel; 1.1 mol H,PO, was produced. Which one of the reactants was in excess, assuming that one of them was.

Ans. 1 rnol H,PO, = 1.3 rnol H,PO,

3mol HCI 3.9 rnol HCI

(

would be produced by reaction of all the HCI. Since the actual quantity of H,PO, produced is 1.1 mol, not all the HCI was used up, and the Na3P0, must be the limiting quantity. The HCI was in excess.

146 STOICHIOMETRY [CHAP. 8

8.47. How much CO, can be produced by the combustion of 1.00 kg of octane, C,H oxygen?

Ans.

in 4.00 kg of

2C,H,,

+

^250,

-

^16C0,

⁺

^18H,O

= 8.77 rnol C,H ^1x present l.OOkgC,H,,(

?)(

1 rnol C,Hl,

= 125mol 0, present

8.77mol C,HI,

(

^{25 mol O2}

)

⁼ 110 mol0, required 2mol C,H,,

Since 110 rnol of O2 is required and 125 rnol 0, is present, the C,H

,,

is in limiting quantity.

8.77 rnol C,H

(

^16m01

)

⁼ 70.2mol CO, produced 2 rnol C,H

,,

44.0g CO,

70.2 rnol CO, = 3 090 g = 3.09 kg CO, produced

8.48. How many grams of CO can be made by burning lOOg C,H,, in lOOg O,?

Ans.

2C,H,,+ 170,-16CO+18H,O

2 rnol C,H

= 0.368 mol C,H,, required

(

^17mol0,

)

3.125 mol0,

Since there is more C,H,, present than is required, the 0, is in limiting quantity.

l6m0l CO

3.125mol0,

(

^17mol

^o, )

⁼ 2.94mol CO produced 28.0g CO

2.94 mol CO( mol

)

^{= 82.3} g CO produced

Supplementary Problems

8.49. Read each of the other supplementary problems and state which ones are limiting quantities problems.

8.50. Calculate the number of grams of methyl alcohol, CH,OH; obtainable in an industrial process from 10.0 X 10hg (10.0 metric tons) of CO plus hydrogen gas.

Ans. See Problem 8.26.

8.51. What percentage of 5.00g KCIO, must be decomposed thermally to produce 1.50g O,?

Ans. The statement of the problem implies that not all the KCIO, is decomposed; it must be in excess for the purposes of producing the 1.50g 0,. Hence we can base the solution on the quantity of 0,.

CHAP. 81 STOICHIOMETRY 147

In Problem 8.37 we found that 3.84g of KCIO, decomposed. The percent KCIO, decomposed is then

(2)

^{x 100% = 76.8%}

8.52. The percent yield is 100 times the amount of a product actually prepared during a reaction divided by the amount theoretically possible to be prepared according to the balanced chemical equation. (Some reactions are slow, and sometimes not enough time is allowed for their completion; some reactions are accompanied by side reactions which consume a portion of the reactants; some reactions never get to completion.) If 3.00g C,HllBr is prepared by treating 3.00g C,H,, with excess Br,, what is the percent yield? The equation is

C,H,,

+

^{Br2 --+ C,H,,Br}

+

^HBr

Ans.

= 0.0356mol C,H,,

= 0.0356mol C,H,,Br 1 rnol C,H,,

84.2g C(jH12 1 mol C,H,,Br

rnol C,H,, 3.00g C,H12

0.0356mol C,H12

= 5.80g C,H,,Br 163g C,H,,Br

rnol C,H,,Br 0.0356 rnol C,H

,

^,Br

x 100 = 51.7% yield 3.00g C,H

,

,Br obtained

5.80 g C,H

,

Br possible

8.53. If 3.00g C,H,,Br is prepared by treating 3.00g C,H,, with 5.00g Br,, what is the percent yield? The equation is

C,H],?

+

^{Br, --+ C,H,,Br}

+

^HBr

Ans.

= 0.0356 rnol C,H 1 rnol C,H]2

84.2g C,H,, 1 rnol Br, 3.00g C,H,2

5.OOg Br,[ 160g B r 2 ) = 0.0312mol Br, Since the reactants react in a 1 : 1 mole ratio, the Br, is in limiting quantity:

= 0.0312mol C,H,,Br

= 5.09g C,HI1Br 1 mol C,H,,Br

rnol Br, 163g C,H,,Br

mol C,H,,Br 0.0312 rnol Br,

0.0312 mol C,H

, ,

^Br

x 100 = 58.9% yield 3.00g C,H,,Br obtained

5.09g C,H,,Br possible 8.54. Make up your own stoichiometry problem using the equation

BaCI,

+

^2AgN0,

-

^Ba(N03),

⁺

^2AgCl

8.55. In a certain experiment, lOOg of ethane, C2H6, is burned. ( a ) Write a balanced chemical equation for the combustion of ethane to produce CO, and water. ( 6 ) Determine the number of moles of ethane in lOOg of ethane. ( c ) Determine the number of moles of CO, that would be produced by the combustion of that number of moles of ethane. ( d ) Determine the mass of CO, that can be produced by the combustion of lOOg of ethane.

148