A chemist performs the following reaction: CS2(s) + 3O2(g) + ---> CO2(g) + 2SO2 (g) If the chemist starts with 125.0 grams of CS2 and an excess of O2, what volume of sulfur dioxide will be...

A chemist performs the following reaction: CS2(s) + 3O2(g) + ---> CO2(g) + 2SO2 (g) If the chemist starts with 125.0 grams of CS2 and an excess of O2, what volume of sulfur dioxide will be produced at a temperature of 149 degrees Celsius and a pressure of 2.3 atm?

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ncchemist's profile pic

ncchemist | eNotes Employee

Posted on

We need to figure out how many moles of SO2 will be produced and then use the gas law equation to convert it to liters (volume).  We start with 125 grams of carbon disulfide (CS2).  Let's convert this to moles.

125 g CS2 * (1 mole/76.139 g) = 1.64 moles CS2

From the reaction equation given in the question, we can see that 1 mole of CS2 produces 2 moles of SO2 assuming there is an excess of oxygen.  So 1.64 moles of CS2 will produce 1.64*2=3.28 moles SO2.  Now let's use the equation PV=nRT to convert the moles of SO2 into liters.  Rearranging to solve for volume (V), we get:

PV=nRT

V=(nRT)/P

where n is the number of moles of SO2 (3.28 moles), R is the gas constant 0.0821 L*atm/mole*K, T is the temperature in units Kelvin (149 C + 273.15 = 422.15 K), and P is pressure (2.3 atm).  Substituting, we get:

V = (3.28 moles * 0.0821 (L*atm/mole*K) * 422.15 K) / 2.3 atm = 49.43 liters SO2.

So 49.43 liters of SO2 are produced.

Sources:
clyoon's profile pic

clyoon | Student, Grade 12 | (Level 1) Salutatorian

Posted on

When you're being asked for info about something in a reaction while being given info about a gas (SO2 in this case), you should refer to the Ideal Gas Law.

PV = nRT

Remember, 

  • P = pressure in atm
  • V = volume in L
  • n = number of moles
  • R = gas constant, 0.0821
  • T = temperature in Kelvins which you find by adding 273 to your value in degrees Celsius

You've been given the number of grams of CS2 but you need info about SO2. You also need to know the number of moles of SO2 to solve for volume using the Ideal Gaw Law equation. So what I'd do is convert the grams of CS2 to moles.

`125.0 g CS2xx(1 mol CS2)/(76.13 g CS2)= 1.64 mol CS2`

1.64 moles is the number of moles you start with of CS2. Now look at the reaction again to see how many moles of SO2 you'll produce. Look at the coefficients in front of CS2 and SO2. The ratio of CS2 to SO2 is 1:2. For every mole of CS2, you will produce 2 moles of SO2. Thus, you need to multiply the CS2 mol value by 2 to get the number of moles of SO2.

`1.64 mol CS2xx 2= 3.28 mol SO2`

Now you can plug in your values to PV=nRT to get your volume

`(2.3)(V) = (3.28)(.0821)(149+273)`

`V = 49 L`

Your volume should be 49 liters because of sig figs. To know how many sig figs you should use, look at your question. The 2 sig figs came from the 2.3 atm value. You should use the smallest number of sig figs when given multiple values in the question.

ayl0124's profile pic

ayl0124 | Student, Grade 12 | (Level 1) Valedictorian

Posted on

First, start off with the Ideal Gas Law.

`PV = nRT`

Plug in your known variables (pressure and temperature). R is the gas constant. I like to look at the units and the only gas constant that has both L and atm is: 0.0821 L atm/K mol. Also note that temperature must be in Kelvins. 

`(2.3 "atm")L = n(0.0821)(149 + 273 "K")`

You have two unknowns now: volume and number of moles. Since, we are solving for volume, we can ignore that for now. The only other information you are given is grams. Use stoichiometry to convert grams of CS2 to moles of SO2.

`125.0 "g" = (1 "mol")/(76.15 "g") = (2 "mol")/(1 "mol") = 3.28 "mol"`

Plug in your "n" and solve for volume.

`(2.3 "atm")L = (3.28 "mol")(0.0821)(149 + 273 "K")` 

`(2.3)L = 113.74`

`L = 49 "L"`

You should get 49 L (with two sig figs!).

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