# Homework Help: Percent Change in Concentration

1. Mar 12, 2015

### henry3369

1. The problem statement, all variables and given/known data
The world burns approximately 3.8 x 1012 kg of fossil fuel per year.

1. Use the combustion of octane as the representative reaction and determine the mass of carbon dioxide (the most significant greenhouse gas) formed per year.

2. The current concentration of carbon dioxide in the atmosphere is approximately 368 ppm (by volume). By what percentage does the concentration increase each year due to fossil fuel combustion? Approximate the average properties of the entire atmosphere by assuming that the atmosphere extends from sea level to 15 km and that it has an average pressure of 381 torr and average temperature of 275 K. Assume Earth is a perfect sphere with a radius of 6371 km.

2. Relevant equations
Volume of a sphere = (4/3)π(r3)
Percent change = (new - old)/old * 100

3. The attempt at a solution
1. 1.2 x 10^6 g

2. Vatm = Vearth+atmosphere - Vearth
Vatm = (4/3)π(63863 - 63713) = 7.66899 x 109 km3 = 7.66899 x 1018 m3

368 ppm = 368 g/m3

Using mass obtained from #1, and finding concentration of the increase in CO2:
1.2 x 1016g/7.66899 x 1018 m3 = 0.001564743 g/m3

New concentration = 368 + 0.001564743
Percent change = (new-old)/old * 100 = 0.00042519%

So the answer is 0.42%, and it seems that the way to achieve this is to have the Vatm = 7.66899 x 1015 m3 rather than 7.66899 x 1018 m3. Is there an error in my volume calculation that I am not catching?

2. Mar 12, 2015

### siddharth23

I didn't go through the entire calculation. But it says 368 ppm by volume, for which you've taken 368 g/m3. But 'g' is a unit of mass. Check that part.

3. Mar 12, 2015

### henry3369

I looked up ppm to g/m^3 and a website told me it was a 1:1 conversion. Can you please tell me what I'm supposed to convert ppm to? I'm familiar with the term.

4. Mar 12, 2015

### henry3369

5. Mar 12, 2015

### siddharth23

Well I'd say that 368 ppm by volume will mean 368 m3 in 1000000 m3. Now that you know the volumes, use the density to find out the amount of CO2 by weight in air. (density = mass / volume)

6. Mar 12, 2015

### henry3369

d = m/V = 44.0087/368 = 0.1196 g/m^3

new concentration = 0.1196 + 000156 = 0.12116

(new-old)/old * 100 = 1.3%

This is incorrect though. What am I doing incorrectly?

7. Mar 13, 2015

### Staff: Mentor

Why do you assume 1 mole of carbon dioxide occupies 368 cubic meters? Just because there are 368 m3 per 1000000 m3? Would you assume volume of 0.368 m3 if you were told 386 ppm means 0.368 m3 in 1000 m3?