Question

What is the volume in liters of $ 6.75 \times {{10}^{24}} $ of molecules of ammonia gas at STP?

Answer 1

Hint :We are going to use the concept of conversion to calculate the solution. As we are going from molecules to volume so we are supposed to convert to moles. For that we need:
Avogadro's number = $ 6.022\times{{10}^{23}} $
Molar Volume of gas at STP = $ 22.71Lmo{{l}^{-1}} $

Complete Step By Step Answer:
In any substance, the number of units in a mole is known as Avogadro’s number or Avogadro’s constant. It is equal to $ 6.022\times{{10}^{23}} $ . The units can be anything such as electrons, ions, atoms or even molecules. It basically depends on the character of the reaction and the nature of that substance.
So, Avogadro’s number is telling us the number of particles in $ 1 $ mole of a substance. And as we already know these particles can be electrons or molecules or atoms. Also, the value of Avogadro’s number is about $ 6.022140857\times {{10}^{23}}\text{ }mo{{l}^{-1}} $
Molar Volume of the gas at STP is given by:
Density of the gas at STP = D
Molar mass of the gas = M
Molar Volume of the gas = V
So, the formula to calculate the molar volume of the gas at STP becomes:
 $ V $ $ = $ $ \dfrac{M}{D} $
The molar volume of gas at STP is $ 22.71Lmo{{l}^{-1}} $ which basically means that there are $ 22.71 $ litres of the gas per mole of a gas.
Here as we are going from molecules to volume so we need to convert it to moles and for that we need Avogadro’s number which is $ 6.022\times{{10}^{23}} $ .
Steps of conversion are:
Moles of gas = $ M $
Avogadro’s number = $ {{N}_{A}} $
No of molecules = $ {{M}_{n}} $
Formula to calculate moles of gas:
 $ {{M}_{n}} $ = $ \dfrac{M}{{{N}_{A}}} $
 $ Moles\text{ }of\text{ }ammonia\text{ }gas $ ( $ {{M}_{n}} $ )= $ \dfrac{No\text{ }of\text{ }molecules({{M}_{n}})}{Avogadro's\text{ }number({{N}_{A}})} $
 $ Moles\text{ }of\text{ }ammonia\text{ }gas $ ( $ {{M}_{n}} $ )= $ \dfrac{6.75\times{{10}^{24}}}{6.022\times{{10}^{23}}} $ moles
 $ Moles\text{ }of\text{ }ammonia\text{ }gas $ ( $ {{M}_{n}} $ )= $ 11.2089... $ moles
Volume of ammonia gas is given by
 $ = $ $ Moles\text{ }of\text{ }ammonia\text{ }gas $ $ \times $ $ molar\text{ }volume\text{ }of\text{ }gas\text{ }at\text{ }STP $
 $ =11.2089...moles\times22.72Lmo{{l}^{-1}} $
 $ =254.55L $
So, the volume of $ 6.75\times{{10}^{24}} $ of molecules of ammonia gas at STP is $ =254.55L $

Note :
You have to carefully calculate the solution step by step, by calculating the number of moles and then multiplying it by the molar volume of gas at STP. So, be very careful with the equations involved.