The diffusion rate for a solute is 4.0 10-11 kg/s in a solvent-filled channel that has a cross-sectional area of 0.50 cm2 and a length of 0.220 cm. What would be the diffusion rate m/t in a channel with a cross-sectional area of 0.30 cm2 and a length of 0.10 cm?
rate is proportional to area and inversely proportional to length
4 * 10*-11 kg/s = k * .5cm^2 /.22
k = 1.76 * 10^-11
rate = 1.76*10^-11*.3/.1
= 5.28 * 10^-11 kg/s
Thank you, Damon. :)
To find the diffusion rate in the new channel, we can use the formula:
Diffusion Rate = (Diffusion Coefficient * Cross-sectional Area) / Length
Given values in the first channel:
Diffusion Rate1 = 4.0 * 10^(-11) kg/s
Cross-sectional Area1 = 0.50 cm^2
Length1 = 0.220 cm
Given values in the second channel:
Cross-sectional Area2 = 0.30 cm^2
Length2 = 0.10 cm
First, let's calculate the Diffusion Coefficient (D) using the first channel:
Diffusion Coefficient = Diffusion Rate1 / (Cross-sectional Area1 / Length1)
D = 4.0 * 10^(-11) kg/s / (0.50 cm^2 / 0.220 cm)
D = 1.76 * 10^(-10) kg/(cm*s)
Now, let's calculate the diffusion rate in the second channel using the Diffusion Coefficient and the given values in the second channel:
Diffusion Rate2 = (D * Cross-sectional Area2) / Length2
Diffusion Rate2 = (1.76 * 10^(-10) kg/(cm*s) * 0.30 cm^2) / 0.10 cm
Diffusion Rate2 = (1.76 * 10^(-10) kg/s) * 3.00
Diffusion Rate2 = 5.28 * 10^(-10) kg/s
Therefore, the diffusion rate in the second channel would be 5.28 * 10^(-10) kg/s.
To calculate the diffusion rate m/t in the second channel, we need to use the equation:
Diffusion rate m/t = (Diffusion rate in channel 1 * Area of channel 1) / (Area of channel 2 * Length of channel 1)
Given values:
Diffusion rate in channel 1 = 4.0 * 10^-11 kg/s
Area of channel 1 = 0.50 cm^2
Area of channel 2 = 0.30 cm^2
Length of channel 1 = 0.220 cm
Let's substitute these values into the equation:
Diffusion rate m/t = (4.0 * 10^-11 kg/s * 0.50 cm^2) / (0.30 cm^2 * 0.220 cm)
To perform the calculation, first convert the cm^2 to m^2 because the diffusion rate is given in kg/s:
Diffusion rate m/t = (4.0 * 10^-11 kg/s * 0.005 m^2) / (0.003 m^2 * 0.0022 m)
Now, multiply the numerator and denominator:
Diffusion rate m/t = (2.0 * 10^-13 kg/s) / (6.6 * 10^-9 m)
Finally, divide 2.0 * 10^-13 kg/s by 6.6 * 10^-9 m:
Diffusion rate m/t ≈ 3.03 * 10^-5 kg/m/s
Therefore, the diffusion rate in the second channel would be approximately 3.03 * 10^-5 kg/m/s.