From a titration of KHP and NaOH.
Determine the range in NaOH volume to achieve a relative standard deviation of less than 0.2%. Assume 800mg of KHP was used.
To determine the range in NaOH volume that will achieve a relative standard deviation of less than 0.2%, we need to calculate the standard deviation of the titration results using the given information.
First, let's define the formula for relative standard deviation (RSD):
RSD = (Standard Deviation / Mean) * 100
In this case, we want RSD to be less than 0.2%, which is equivalent to 0.002 in decimal form. Let's assume the mean volume of NaOH required to titrate 800mg of KHP is X mL.
To calculate the standard deviation, we need multiple titration results. However, since you haven't provided that information, let's assume you conducted 5 titrations and obtained volumes of NaOH (in mL) required for each titration: A1, A2, A3, A4, and A5.
Step 1: Calculate the mean volume of NaOH.
Mean Volume (X) = (A1 + A2 + A3 + A4 + A5) / 5
Step 2: Calculate the sum of the squared differences between each volume and the mean volume.
Sum of Squared Differences = (A1 - X)^2 + (A2 - X)^2 + (A3 - X)^2 + (A4 - X)^2 + (A5 - X)^2
Step 3: Calculate the variance.
Variance = Sum of Squared Differences / (n - 1)
Note: (n - 1) represents the degrees of freedom, which is the number of independent observations minus 1. In this case, since we assumed 5 titrations, the degrees of freedom would be 5 - 1 = 4.
Step 4: Calculate the standard deviation.
Standard Deviation = √Variance
Step 5: Calculate the relative standard deviation (RSD).
RSD = (Standard Deviation / Mean Volume) * 100
Now, we can substitute the given values into the formula and solve for X to determine the range in NaOH volume.
Let's say we solve the calculations and find that the mean volume of NaOH is X mL. The range in NaOH volume would be within ±0.2% (or ±0.002) of the mean volume. Therefore, the range would be (X - 0.002X) to (X + 0.002X).
To express this in terms of mL:
Range (in mL) = X * 0.998 to X * 1.002
Note: The actual numerical values will depend on the experimental data and calculations. Make sure to substitute the appropriate values when performing the calculations.