Carbon Dioxide Diffusion#

According to our textbook, at 25$$^\circ$$ $$C$$, the diffusion constant of $$CO_2$$ in water is $$D\_{water} = {{ params.water }} \times 10^{-9}$$ $$m^2/s$$ and the diffusion constant of $$CO_2$$ in air at one atmosphere is $$D\_{air} = {{ params.air }} \times 10^{-5}$$ $$m^2/s$$. If it takes $$t\_{air} =$$ 6 $$s$$ for $$CO_2$$ to diffuse a distance $$r\_{rms}=d_1$$ through the air, how long does it take for $$CO_2$$ to diffuse $$r\_{rms}=d_1$$ through the water?

Part 1#

Prepare: Write a formula for the diffusion time $$t$$ in terms of the distance $$d_1$$ and diffusion constant $$D$$ given that $$r\_{rms}=\sqrt{ {{ params.const }} Dt}$$.

Note that it may not be necessary to use every variable. Use the following table as a reference for using each variable:

For

Use

$$d_1$$

d1

$$D$$

D

Part 2#

Prepare: Use proportional reasoning to express $$\frac{t\_{water}}{t\_{air}}$$ in terms of $$D\_{water}$$ and $$D\_{air}$$.

Note that it may not be necessary to use every variable. Use the following table as a reference for using each variable:

For

Use

$$D\_{water}$$

D_w

$$D\_{air}$$

D_a

Part 3#

Prepare: In this problem, are $$t$$ and $$D$$ directly or inversely proportional?

• directly

• inversely

Part 4#

Solve for $$t\_{water}$$ numerically.

Answer Section#

Please enter in a numeric value in $${{ params.vars.unit2 }}$$.

Part 5#

Assess: Does your answer make sense in the context of carbonated water being something people drink? Explain your answer.

Answer Section#

Answer in 2-3 sentences, try and use full sentences.

Attribution#

Problem is licensed under the CC-BY-NC-SA 4.0 license.