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 \(t\_{air} = \) 5 \(s\) 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.
The Creative Commons 4.0 license requiring attribution-BY, non-commercial-NC, and share-alike-SA license.