Uncertainty In Measurement - Practice Questions & MCQ

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DIFFICULT

The minimum amount of $O_{2}\left ( g \right )$ consumed per gram of reactant is for the reaction :

(Given atomic mass : $Fe=56,$ $O=16$ , $Mg=24,P=31,C=12,H=1$ )

$4Fe\left ( s \right )+3O_{2}\left ( g \right )\rightarrow 2Fe_{2}O_{3}\left ( s \right )$

$P_{4}\left ( s \right )+5O_{2}\left ( g \right )\rightarrow P_{4}O_{10}\left ( s \right )$

$C_{3}H_{8}\left ( g \right )+5O_{2}\left ( g \right )\rightarrow 3CO_{2}\left ( g \right )+4H_{2}O\left ( I \right )$

$2Mg\left ( s \right )+O_{2}\left ( g \right )\rightarrow 2MgO\left ( s \right )$

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UNCERTAINTY IN MEASUREMENT

Scientific Notation

For denoting extremely low masses present in extremely large numbers as large as 602,200,000,000,000,000,000,000 for the molecules of 2 g of hydrogen gas or as small as 0.00000000000000000000000166 g mass of an H atom, need to use scientific notation i.e., exponential notation in which any number can be represented in form N × 10ⁿ where n is an exponent having positive or negative values and N is a number (called digit term) which varies between 1.000... and 9.999.... Thus, we can write 232.609 as 2.32609 ×10² in scientific notation.

Addition and Subtraction

For adding or subtracting two numbers

4.5 X 10⁴ + 2.5 X 10⁵ = 4.5 X 10⁴ + 25.0 X 10⁴ = 29.5 X 10⁴

4.5 X 10⁴ - 2.5 X 10⁵ = 4.5 X 10⁴ - 25.0 X 10⁴ = (-)20.5 X 10⁴ (negative)

Multiplication and Division

For multiplying or dividing two numbers

(4.5 X 10⁴) X (2.5 X 10⁵) = (4.5 X 2.5)X (10⁴⁺⁵) = 11.25 X 10⁹ = 1.125 X 10¹⁰

(4.5 X 10⁴ ) / (2.5 X 10⁵) = (4.5 / 2.5) X 10^4-5 = 1.8 X 10^-1

Significant Figures

Precision refers to the closeness of various measurements for the same quantity.

Accuracy is the agreement of particular value to the true value of the result.

The uncertainty in the experimental or the calculated values is indicated by mentioning the number of significant figures. Significant figures are meaningful digits that are known with certainty. The uncertainty is indicated by writing the certain digits and the last uncertain digit.

There are certain rules for determining the number of significant figures. These are stated below:

(1) All non-zero digits are significant.

(2) Zeros preceding to first non-zero digit are not significant. Such zero indicates the position of the decimal point.

(3) Zeros between two non-zero digits are significant.

(4) Zeros at the end or right of a number are significant provided they are on the right side of the decimal point.

(5) Counting numbers of objects, for example, 2 balls or 20 eggs, have infinite significant figures as these are exact numbers and can be represented by writing an infinite number of zeros after placing a decimal i.e., 2 = 2.000000 or 20 = 20.000000

In numbers written in scientific notation, all digits are significant e.g., 4.01×10² has three significant figures, and 8.256 × 10^–3 has four significant figures.

Dimensional Analysis

While calculating, the units should be the same all across the equation The units for each physical quantity should be the same throughout the equation.

eg. If the temperature is involved, the units should be Kelvin on both sides