Tag: uncertainties and errors, graphical techniques

Questions Related to uncertainties and errors, graphical techniques

Which set of figures will be obtained after rounding up the following upto three significant figures?
34.216,  0.04597, 10.4107

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. 34.3, 0.0461, 10.4

  2. 34.2, 0.0460, 10.4

  3. 34.20, 0.460, 10.40

  4. 34.21, 4.597, 1.04

Show answer
Correct Option: B
Explanation:

To round up a given number, ignore the last digit as such if the digit next to it is less than 5. Then increase it by 1, if the next digit is greater than 5.

(i) 34.216

34.22 { since next digit (6) is greater than 5 }

34.2 {since next digit (2) is less than 5 }

 (ii) 0.04597

0.0460 {since next digit (7) is greater than 5}

(iii) 10.4107

10.411 { since next digit (7) is greater than 5}

10.41 { since next digit (1) is less than 5}

10.4 { since next digit (1) is less than 5}

Thus option B is correct.

Few figures are expressed in scientific notation. mark the incorrect one.

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. $234000 = 2.34 \times 10^5$

  2. $8008 = 8 \times 10^3$

  3. $0.0048 = 4.8 \times 10^{-3}$

  4. $500.0 = 5.00 \times 10^2$

Show answer
Correct Option: B
Explanation:

Figures in scientific notation will be:

A. $234000=2.34 \times 10^5$ 

B. $8008=8.008 \times 10^3 $

C. $0.0048=4.8 \times 10^{−3}$

D. $500.0=5.00 \times 10^2$

Which of the following rules regarding the significant figures and calculations involving them is not correct?

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. The result of an addition or subtraction is reported to the same number of decimal places as present in number with least decimal places.

  2. Result of multiplication or division should have same number of significant figures as present in most precise figure

  3. The result of multiplication or division should be rounded off to same number of significant figures as present in least precise figure.

  4. The non-significant figures in the measurements are rounded off.

Show answer
Correct Option: B
Explanation:
1. The result of an addition or subtraction is reported to the same number of decimal places as present in number with the least decimal places.
2. The result of multiplication or division should be rounded off to the same number of significant figures as present in number with the least significant number.
3. The result of multiplication or division should be rounded off to the same number of significant figures as present in the least precise figure.
4. The non-significant figures in the measurements are rounded off.
option B is correct

Magnitude of $e/m$ for ${O^ - }$

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. $10^{-12}$

  2. $10^{-20}$

  3. $10^{-22}$

  4. $10^{-18}$

Show answer
Correct Option: B
Explanation:

Here: Mass of ${O^ - } = 16\,g/mol$ and

charge ${O^ - } = {\text{one unit}}$

$ = 1.6 \times {10^{ - 19}}C$

So,

$e/m = \dfrac{{{\text{Charge}}}}{{{\text{Mass}}\,{\text{ratio}}}}$

$ = \dfrac{{1.6 \times {{10}^{ -19}}C}}{{16\,g/mol}}$

$ = \dfrac{{1.6 \times {{10}^{ - 19}}\times C \times mol}}{{16\,g}}$

$ = \dfrac{{0.1 \times {{10}^{ - 19}}\times C \times NA}}{g}\,\,\,\,\,\,\,\,\,\boxed{mol = NA}$

$e/m = {10^{ - 20}}\dfrac{C}{g}$

Two students are working on an AP Chemistry lab. Their assignment is to determine experimentally the density of a nonvolatile organic liquid, limestone. The accepted value for the density of limestone is $0.8422\ g/mL$. Each student conducts three separate density determinations, then calculates a mean (average) value for the density and the standard deviation for their three trials.

Student A Student B
Density #$1$ $0.8421 g/mL$ $0.8408 g/mL$
Density #$2$ $0.8514 g/mL$ $0.8502 g/mL$
Density #$3$ $0.8355 g/mL$ $0.8332 g/mL$
Mean Density $0.8430 g/mL$ $0.8414 g/mL$
Standard Deviation $0.0080$ $0.0085$

The results and calculations for each students are shown in the table below.
Of the four descriptions given below, which BEST interprets the accuracy and precision of Student A and Student B?

chemistry measurement and data processing and analysis uncertainties and errors, graphical techniques uncertainty in measurement measurement of properties

  1. Student A and Student B are equally precise, but Student B has more accurate results.

  2. Student A and Student B are equally accurate, but Student B has more precise results.

  3. Student A and Student B have equal accuracy and equal precision.

  4. Student A has more accurate and more precise results than Student B.

Show answer
Correct Option: B