Question

the thermodynamics of ethanol
percent error
the researchers calculated value for the enthalpy of formation was -187 kj/mol.
the accepted value for enthalpy of formation is -277 kj/mol.
what is the percent error for the experiment?
-32%
-48%
32%
48%

Explanation:

Step1: Recall the percent error formula

The formula for percent error is $\text{Percent Error} = \frac{|\text{Measured Value} - \text{Accepted Value}|}{|\text{Accepted Value}|} \times 100\%$. Here, the measured (calculated) value is $- 187\space kJ/mol$ and the accepted value is $-277\space kJ/mol$.

Step2: Calculate the difference

First, find the difference between the measured and accepted values: $-187 - (-277)=- 187 + 277 = 90$. Take the absolute value: $|90| = 90$.

Step3: Calculate the absolute value of the accepted value

The absolute value of the accepted value $|-277|=277$.

Step4: Compute the percent error

Now, plug into the formula: $\text{Percent Error}=\frac{90}{277}\times100\%\approx 32\%$. Since the measured value is higher than the accepted value (because $- 187>-277$), the error is positive in terms of magnitude (we take absolute values in the formula, but the sign here comes from the fact that the measured value is above the accepted one, but the percent error formula gives a positive value when the measured is higher than accepted in magnitude? Wait, no, the formula is $\frac{|\text{measured}-\text{accepted}|}{|\text{accepted}|}\times 100\%$. So regardless of the signs of measured and accepted, we take the absolute difference over absolute accepted value. So in this case, the calculation gives approximately $32\%$.

Answer:

32% (corresponding to the option "32%")