Chapter 3, Problem 19STP

Interpretation Introduction

Interpretation:

Percentage error in another experiment, a sample of acetic acid consists of $56.8\%$ oxygen.

Concept introduction:

Difference between experimental value and accepted value is defined Error. Formula of percentage error is used to calculate slight manufacturing errors in measuring instruments, which is 

$\text{\%}\text{Error}\text{=}\frac{\text{Experimental}\text{value}\text{-}\text{Accepted}\text{value}}{\text{Accepted}\text{value}}\text{×100}$

Answer to Problem 19STP

Correct answer: Option (b ), $6.57\%$

Explanation of Solution

Reason for correct option:

The known table is:

Percentage by mass of carbon, hydrogen, and oxygen in selected compounds
Compound	%H	%C	%O
Carbonic acid	$3.2$	$19.4$	$77.4$
Acetic acid	$6.7$	$40.0$	$53.3$
Methanol	$12.5$	$37.5$	$40.0$
Methanol	$6.7$	$40.0$	$53.3$
Isopropanol	$13.3$	$60.0$	$26.7$

The experimental value is $56.8$ and accepted value is $53.3$ from the given table,

So for the calculation of percentage error-

$\text{\%}\text{Error}\text{=}\frac{\text{experimental}\text{value}\text{-}\text{accepted}\text{value}}{\text{accepted}\text{value}}\text{×100}$

$\text{\%}\text{Error}\text{=}\frac{\text{(56}\text{.8}\text{-}53.3\text{)}}{53.3}\text{×100}$

$=6.5666\%$ = $6.57\%$

The percentage error for the sample is $6.57\%$. Hence, this is the correct option.

Conclusion

Reasons for incorrect options:

Option (a) the given option, $3.50\%$, is not equal to the calculated value, $6.57\%$. Hence, this is an incorrect option.

Option (c)the given option, $1.07\%$, is not equal to the calculated value, $6.57\%$. Hence, this is an incorrect option.

Option (d) the given option, $12.6\%$, is not equal to the calculated value, $6.57\%$. Hence, this is an incorrect option.

Option (e) the given option, $2.06\%$, is not equal to the calculated value, $6.57\%$. Hence, this is an incorrect option.