Question

A sample of gas occupies \[{\text{240 c}}{{\text{m}}^{\text{3}}}\] at \[{\text{37}}{{\text{ }}^{\text{o}}}{\text{C}}\] and \[{\text{100 kPa}}\]. How many moles of gas are present in the sample?
A. \[9.32{\text{ }} \times {10^{ - 3}}\]
B. \[1.24{\text{ }} \times {10^{ - 3}}\]
C. \[0.0781\]
D. \[78.1\]

Answer 1

Hint: We must know that the ideal gas law is the empirical relationship between volume and the amount of gas. Therefore, we can solve this question with the ideal gas equation
\[{\text{PV = nRT}}\]
Formula used:
The ideal gas equation is
\[{\text{PV = nRT}}\]
Where,
\[P\] is pressure
\[V\] is volume
\[R\] is gas constant
\[T\] is temperature
\[n\] is the number of moles

Complete step by step answer:
In the question, they have given
\[
  P = 100k \\
  {P_a} = 0.987atm{\text{ }}\left( {\because 1atm = 101.325kPa} \right) \\
 \]
\[V = 240c{m^3} = 0.24L{\text{ }}(Q1c{m^3} = {10^{ - 3}}L)\]
\[T = {37^o}C = 273.15 + 37 = 310.15K\]
R= Gas constant =\[{\text{0}}{\text{.0821L}}{\text{.atm/mol}}{\text{.K}}\]
According to ideal gas law,\[{\text{PV = nRT}}\], where ‘n’ is the number of moles of the molecules.
Therefore, we can substitute the value of pressure (P), volume (V) and temperature (T) in the ideal gas equation; we can find the value of ‘n’
\[PV = nRT\]
\[0.987 \times 0.24 = n \times 0.0821 \times 310\]
\[n = 9.3 \times {10^{ - 3}}{\text{mol}}\]
Therefore, option A. \[9.32{\text{ }} \times {10^{ - 3}}\] is the correct among the following.

Note:
We can define the mole as the amount of a substance that contains exactly \[6.02214076{\text{ }} \times {10^{23}}\;\]‘elementary entities’ of the given substance that can be atoms, molecules, monatomic/polyatomic ions, and other particles (such as electrons).
The number \[6.02214076{\text{ }} \times {10^{23}}\;\] is popularly known as the Avogadro constant and is often denoted by the symbol ‘\[{N_A}\]’.
Also one mole of carbon-12 (\[^{12}C\]) sample will have a mass of exactly equal to 12 grams and will contain \[6.02214076{\text{ }} \times {10^{23}}\;\] (\[{N_A}\]) number of \[^{12}C\] atoms. The number of moles of a given substance can also be represented by the following formula:
\[{\text{n = N/}}{{\text{N}}_{\text{A}}}\]
Where ‘n’ is the number of moles of the substance (or elementary entity), N is the total number of elementary entities in the sample, and \[{N_A}\] is the Avogadro constant.