Question

Volume of gas at NTP is $ 1.12 \times {10^{ - 7}}c{m^{ - 3}} $ . Calculate the number of molecules in it.
(A) $ 3.01 \times {10^{12}} $
(B) $ 3.01 \times {10^{20}} $
(C) $ 3.01 \times {10^{24}} $
(D) $ 3.01 \times {10^{23}} $

Answer 1

Hint: NTP stands for Normal. Temperature and Pressure. We have given the volume of gas at NTP so to calculate the number of molecules in the gas we will use the basic chemistry of mole concept that $ 22.4L $ gas at NTP produces or corresponds to one mole.

Complete step by step answer:
First, we will understand what is given to us in the question and what we need to calculate. So, the question says that Volume of gas at NTP is $ 1.12 \times {10^{ - 7}}c{m^{ - 3}} $ which gives us that the volume of gas at Normal, Temperature, and pressure the total molecules or the moles of gas acquires the volume of $ 1.12 \times {10^{ - 7}}c{m^{ - 3}} $ . So, now if we calculate the volume of the gas at Normal, Temperature and Pressure which correspond to one mole of the gas we can easily calculate the number of molecules which requires the volume of gas at Normal, Temperature and Pressure which equals to $ 1.12 \times {10^{ - 7}}c{m^{ - 3}} $ .
We know that $ 22.4L $ gas at NTP produces or corresponds to one mole. In chemistry, we know that one mole of an atom contains $ 6.02 \times {10^{23}} $ molecules or particles. The value of $ 6.02 \times {10^{23}} $ molecules or particles represents Avogadro's number. Avogadro’s number is represented by $ {N_A} $ . So, now we know that $ 22400c{m^{ - 3}} $ gas corresponds to $ 6.02 \times {10^{23}} $ molecules or particles. So the number of molecules in $ 1.12 \times {10^{ - 7}}c{m^{ - 3}} $ of gas will be $ \dfrac{{6.02 \times {{10}^{23}}}}{{22400}} = 3.01 \times {10^{12}} $ molecules.
Therefore, the correct option is (A).

Note:
There is a basic difference between NTP and STP is that STP stands for standard, Temperature, and pressure, and the values at STP are set by IUPAC as $ T = 273.15K $ and the pressure is $ 1 $ bar or $ 100KPa $ and NTP is set at $ T = 293.15K $ and pressure at $ 101.325KPa $ .