Question

1. a student decides it is possible to estimate the capacity of a test tube by treating it as a rectangle and neglecting its

oundness\. on this basis, the student finds the capacity of the test tube to be 100.5 ml. in fact, the real capacity of the test tube is 100.0 ml. what percent error has resulted from the students assumption?

1. a chemist attempts to determine the surface tension of various detergent - containing liquids by using a tensiometer. in determining the accuracy of the instrument, the chemist tests the surface tension of pure water and obtains a value of 71.28 dynes cm. the standard value for surface tension of pure water is 71.97 dynes cm. what is the percent error of the tensiometer?
2. in an exercise to teach students how to use and analytical balance, the instructor gives a student a quarter which has been pre - weighed as 5.6026 g. the weight that the student obtains for the same quarter is 5.6013 g. what is the percent error in the students reading?
3. the concentration determined for an unknown sample of hydrochloric acid by a student is 0.1355 m. according to the instructors information, the true molarity (m) of this solution is 0.1364 m. what is the percent error in this experiment?
4. an object with a pre - weighed mass of exactly (and correctly) 0.54 g is given to 2 students. one student obtains a weight of 0.59 g for the object, while another says the weight is 0.49 g. which of the students, if either has the greater percent error?

Explanation:

Step1: Recall percent - error formula

The percent - error formula is $\text{Percent Error}=\frac{\vert\text{Experimental Value}-\text{True Value}\vert}{\text{True Value}}\times100\%$.

Step2: Solve problem 6

The experimental value of the test - tube capacity is $V_{exp}=100.5$ ml and the true value is $V_{true}=100.0$ ml.
$\text{Percent Error}=\frac{\vert100.5 - 100.0\vert}{100.0}\times100\%=\frac{0.5}{100.0}\times100\% = 0.5\%$

Step3: Solve problem 7

The experimental value of the surface tension of pure water is $\gamma_{exp}=71.28$ dynes/cm and the true value is $\gamma_{true}=71.97$ dynes/cm.
$\text{Percent Error}=\frac{\vert71.28 - 71.97\vert}{71.97}\times100\%=\frac{\vert - 0.69\vert}{71.97}\times100\%\approx0.96\%$

Step4: Solve problem 8

The experimental value of the quarter's weight is $m_{exp}=5.6026$ g and the true value is $m_{true}=5.6013$ g.
$\text{Percent Error}=\frac{\vert5.6026 - 5.6013\vert}{5.6013}\times100\%=\frac{0.0013}{5.6013}\times100\%\approx0.023\%$

Step5: Solve problem 9

The experimental value of the molarity of the HCl solution is $M_{exp}=0.1355$ M and the true value is $M_{true}=0.1364$ M.
$\text{Percent Error}=\frac{\vert0.1355 - 0.1364\vert}{0.1364}\times100\%=\frac{\vert - 0.0009\vert}{0.1364}\times100\%\approx0.66\%$

Step6: Solve problem 10

For the first student:
The experimental value is $m_{1exp}=0.59$ g and the true value is $m_{true}=0.54$ g.
$\text{Percent Error}_1=\frac{\vert0.59 - 0.54\vert}{0.54}\times100\%=\frac{0.05}{0.54}\times100\%\approx9.26\%$
For the second student:
The experimental value is $m_{2exp}=0.49$ g and the true value is $m_{true}=0.54$ g.
$\text{Percent Error}_2=\frac{\vert0.49 - 0.54\vert}{0.54}\times100\%=\frac{\vert - 0.05\vert}{0.54}\times100\%\approx9.26\%$
The percent errors are equal.

Answer:

1. $0.5\%$
2. $\approx0.96\%$
3. $\approx0.023\%$
4. $\approx0.66\%$
5. The percent errors are equal, approximately $9.26\%$ for both students.