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# 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. $78.1$

Last updated date: 22nd Jun 2024
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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

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.