Question

4.48 litres of methane at N.T.P corresponds to:
(A) $1.2\times {{10}^{22}}$ molecules of methane
(B) 0.5 mole of methane
(C) 3.2g of methane
(D) 0.1 mole of methane

Answer 1

Hint: At NTP, 1 mole of any gas corresponds to 22.4litres. Use this to find the number of moles of methane in 4.48 litres. To convert the number of moles into molecules you have to multiply it by the Avogadro’s number. To convert the number of moles in grams, you have to multiply it by the molar mass of the gas.

Complete step by step solution:
We know that NTP is normal temperature and pressure which is set as 101.325 kPa and ${{20}^{{}^\circ }}$ Celsius temperature. At NTP, the volume of one mole of any gas is given as 22.4 litres.
Now, using this we can convert 4.48 litres of methane at NTP.
We know that 22.4 litres of methane will contain one mole of methane.
Therefore, 1litre of methane will have $\dfrac{1}{22.4}$ moles of methane.
Therefore, 4.48 litre of methane will have $\dfrac{1}{22.4}\times 4.48$ moles of methane.
If we calculate this, we will get 0.2 moles of methane.
Now, let us go through the options and see if they are correct or not.

In the first option, we have $1.2\times {{10}^{22}}$ molecules of methane. To convert the moles into the molecule by multiplying it by the Avogadro’s number.
Therefore, 0.2moles of methane will have $0.2\times 6.022\times {{10}^{23}}$ molecules of methane that is $1.2\times {{10}^{23}}$ molecules of methane. Therefore, this option is incorrect.

In the next option, we have 0.5 mole of methane which is incorrect because we have already calculated this above and it has 0.2moles of methane.
Then we have 3.2g of methane. Now to convert 0.2 moles to grams, we have to multiply the number of moles by its molar mass.

We know that methane is $C{{H}_{4}}$. The atomic weight of carbon is 12 and that of hydrogen is 1. So for 4 hydrogen atoms, it is 4. So, the molar mass of methane is 12+4 i.e. 16.
Now, 0.2 mol $\times $ 16g/mol = 3.2g. Therefore, this option is correct.

And lastly, we have 0.1 mole of methane which is incorrect because we have 0.2 moles of methane.
We can understand from the above discussion that 4.48 litres of methane at N.T.P corresponds to 3.2g of methane.

Therefore, the correct answer is option (C) 3.2g of methane.

Note: We should not be confused between NTP and STP. NTP is normal temperature and pressure whereas STP is standard temperature and pressure. STP is set by IUPAC which is the International Union of Pure and Applied Chemistry as ${{0}^{{}^\circ }}$ Celsius and 100 kPa or 1 bar. NTP is set as 101.325 kPa and ${{20}^{{}^\circ }}$ Celsius temperature.