Before determining the amount of sodium carbonate in a sample by titration with standard hydrochloric avid the anaylst decide to check the procedure by analyzing a known sample of 98.75 (w/w)% purity. Five replicate determinations of the known gave the following results: 98.71% 98.59% 98.62% 98.44% 98.58%

At the 95% confidence interval is there any evidance that the analysis is giving inaccurate results?

To determine if there is any evidence of inaccurate results in the analysis, we can calculate the mean and confidence interval using the given data.

1. Calculate the mean of the five replicate determinations:
Mean = (98.71% + 98.59% + 98.62% + 98.44% + 98.58%) / 5
= 98.588%

2. Calculate the standard deviation (SD) of the five replicate determinations:
a. Calculate the squared deviation of each determination from the mean:
Deviation^2 = (98.71% - 98.588%)^2 + (98.59% - 98.588%)^2 + (98.62% - 98.588%)^2 + (98.44% - 98.588%)^2 + (98.58% - 98.588%)^2
= 0.000144% + 0.000004% + 0.000036% + 0.000144% + 0.000004%
= 0.000332%

b. Calculate the variance by dividing the sum of squared deviations by (n - 1), where n is the number of determinations:
Variance = 0.000332% / (5 - 1)
= 0.000332% / 4
= 0.000083%

c. Calculate the standard deviation by taking the square root of the variance:
SD = √0.000083%
= 0.00911%

3. Calculate the confidence interval:
The confidence interval is based on the t-distribution, which requires the degrees of freedom (df). In this case, df = n - 1 = 5 - 1 = 4.

a. Look up the t-value for a 95% confidence level and 4 degrees of freedom (from a t-distribution table or calculator). Let's assume it is 2.776.

b. Calculate the margin of error (ME):
ME = t-value * (SD / √n)
= 2.776 * (0.00911% / √5)
= 0.00652%

c. Calculate the lower and upper bounds of the confidence interval:
Lower bound = Mean - ME
= 98.588% - 0.00652%
= 98.581%

Upper bound = Mean + ME
= 98.588% + 0.00652%
= 98.595%

4. Interpret the confidence interval:
Since the known sample has a purity of 98.75% (w/w), any results within the confidence interval should be considered accurate. In this case, the calculated confidence interval (98.581% to 98.595%) includes the expected purity of 98.75%. Therefore, there is no strong evidence to suggest that the analysis is giving inaccurate results at the 95% confidence level.