Glycerin in water diffuses along a horizontal column that has a cross-sectional area of 2.3cm^2. The concentration gradient is 0.028 kg/m^4, and the diffusion rate is found to be 5.8 x 10 ^-15 kg/s find the diffusion coefficient in units of m^2/s.
I get 9.00621 x 10 ^-11 m^2/s but the computer says that is wrong. I used the equation, Diffusion rate = DA (concentration gradient) where A is area and D is what we are looking for.
To find the diffusion coefficient, we can use Fick's law of diffusion, which states:
Diffusion Rate = -D * A * (∆C/∆L)
Where:
- Diffusion Rate is the rate at which molecules diffuse (given: 5.8 x 10^-15 kg/s)
- D is the diffusion coefficient we want to find (in m^2/s)
- A is the cross-sectional area (given: 2.3 cm^2 = 2.3 x 10^-4 m^2)
- ∆C is the difference in concentration (given: 0.028 kg/m^4)
- ∆L is the distance over which diffusion occurs (unknown)
Rearranging the equation to solve for D:
D = -Diffusion Rate / (A * (∆C/∆L))
Now we need to find the value of ∆L. Since the problem states that diffusion occurs "along a horizontal column," we can assume that ∆L is the thickness or height of the column. However, this value is not provided in the given information.
If you have any additional information or assumptions about the thickness of the column, I can calculate the diffusion coefficient for you.
To find the diffusion coefficient in units of m²/s, we can use Fick's first law of diffusion, which states that the diffusion rate is equal to the diffusion coefficient multiplied by the cross-sectional area of the column multiplied by the concentration gradient.
The formula can be written as:
Diffusion Rate = Diffusion Coefficient * Cross-Sectional Area * Concentration Gradient
In this case, we have the following values given:
Diffusion Rate = 5.8 x 10^-15 kg/s
Cross-Sectional Area = 2.3 cm² = 2.3 x 10^-4 m²
Concentration Gradient = 0.028 kg/m^4
Substituting these values into the formula, we have:
5.8 x 10^-15 kg/s = Diffusion Coefficient * 2.3 x 10^-4 m² * 0.028 kg/m^4
Now, let's solve for the diffusion coefficient.
First, rearrange the equation to isolate the diffusion coefficient:
Diffusion Coefficient = Diffusion Rate / (Cross-Sectional Area * Concentration Gradient)
Plugging in the given values:
Diffusion Coefficient = (5.8 x 10^-15 kg/s) / (2.3 x 10^-4 m² * 0.028 kg/m^4)
Now, let's perform the calculation:
Diffusion Coefficient ≈ 1.36 x 10^-4 m²/s
Therefore, the diffusion coefficient in units of m²/s is approximately 1.36 x 10^-4 m²/s.