Freundlich gave the following data fro adsorption of acetic acid on charcoal. obtain the constant k and n in the Freundlich adsorption isotherm; x/m=kc^1/n.
c x/m
0.0181 0.457
0.0616 0.801
0.2677 1.55
0.8817 2.84
2.785 3.76
Just using the first two data points, I get
k = 2.8724
n = 2.1825
Do you need to do a best-fit regression?
To obtain the constant k and n in the Freundlich adsorption isotherm equation, you need to perform a linearization of the data points. The equation given is x/m = kc^(1/n), where x is the amount of adsorbate adsorbed, m is the mass of the adsorbent, c is the concentration of the adsorbate, k is the adsorption constant, and n is the Freundlich exponent.
To linearize the equation, take the logarithm of both sides:
ln(x/m) = ln(k) + (1/n)ln(c)
By plotting ln(x/m) on the y-axis and ln(c) on the x-axis, the resulting graph will be a straight line with slope (1/n) and y-intercept ln(k). Calculating these values will give you the constant k and n.
To obtain the values of ln(x/m) and ln(c), you can use a scientific calculator, spreadsheet software like Microsoft Excel, or online tools. After calculating ln(x/m) and ln(c), plot ln(x/m) as a function of ln(c) and determine the slope and y-intercept of the best-fit line.
Here are the calculated values of ln(x/m) and ln(c) using the given data:
c x/m ln(x/m) ln(c)
0.0181 0.457 -0.782 -4.013
0.0616 0.801 -0.221 -2.789
0.2677 1.55 0.437 -1.316
0.8817 2.84 1.043 -0.123
2.785 3.76 1.325 1.026
Plotting ln(x/m) against ln(c), you will get a straight-line graph. Calculate the slope and y-intercept of this line using linear regression analysis or any appropriate method.
Assuming you perform the linear regression analysis and find that the slope is 1/n and the y-intercept is ln(k), then the values for k and n in the Freundlich adsorption isotherm for acetic acid adsorption on charcoal in this specific case will be:
k = e^(y-intercept)
n = 1 / slope
Substitute the calculated values into these formulas to get the values for k and n in the Freundlich equation.