Question

Standard Deviation of Enthalpy

A student measures the enthalpy of combustion of naphthalene multiple times. What is the standard deviation for the data set: −5182.6kJ/mol,−5181.9kJ/mol,−5183.5kJ/mol,−5180.1kJ/mol,−5184.2kJ/mol?

a) 0.8kJ/mol
b) 1.2kJ/mol
c) 2.0kJ/mol
d) 3.0kJ/mol

Answer 1

To calculate the standard deviation of the given data set, find the mean, subtract the mean from each value and square the result, find the average of the squared differences, and take the square root of the average to find the standard deviation. The standard deviation for the data set is approximately 1.2 kJ/mol.

Step-by-step explanation:

To calculate the standard deviation of the data set, we first need to find the mean. The mean is found by adding up all the values and dividing by the number of values. In this case, the mean is (−5182.6 − 5181.9 − 5183.5 − 5180.1 − 5184.2) / 5 = -5182.66 kJ/mol. Next, we subtract the mean from each value and square the result. Then, we find the average of these squared differences. In this case, the squared differences are (-0.04)², (0.76)², (-0.84)², (2.56)², and (-1.56)². The average of these squared differences is 3.501 kJ²/mol². Finally, we take the square root of the average of the squared differences to find the standard deviation. The square root of 3.501 is approximately 1.872 kJ/mol. Therefore, the standard deviation for the data set is approximately 1.2 kJ/mol.