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

Answer Section

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

Answer Section

Part 3

Prepare: In this problem, are \(t\) and \(D\) directly or inversely proportional?

Answer Section

• 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.