Question

Find:
(a) The total number of protons
(b) The total mass of protons in 34 mg of NH3 at STP.
Will the answer change if the temperature and pressure are changed?

Answer 1

Hint: One mole of any atom or molecule contains Avogadro number of atoms in it. Means
One mole = $6.023\times {{10}^{23}}$ atoms.
Avogadro number is going to indicate with a symbol N.

Complete step by step answer:
- In the question it is asked to find the total number of protons and total mass of the protons in 34 mg of ammonia at STP.
(a) - The molecular weight of the ammonia is 17 g.
- First we will calculate the number of moles present in 34 mg of ammonia.
- Number moles in 34 mg or 0.034 g of ammonia is the ratio of mass to the molecular weight.
- Then
\[\begin{align}
  & =\dfrac{0.034}{17} \\
 & =0.002moles \\
\end{align}\]
- We know that one mole of ammonia = $6.023\times {{10}^{23}}$ molecules of ammonia.
- Then 0.002 moles of ammonia contains
\[\begin{align}
  & =0.002\times 6.023\times {{10}^{23}} \\
 & =1.2046\times {{10}^{21}}\text{molecules of ammonia} \\
\end{align}\]
- Means 0.002 moles of ammonia contains $1.2046\times {{10}^{21}}$ molecules of ammonia.
- We know that one molecule of ammonia contains 10 protons (N = 7 protons, H = 1 proton, 7+3 =10).
- Therefore the protons present in $1.2046\times {{10}^{21}}$ molecules of ammonia is
\[\begin{align}
  & =1.2046\times {{10}^{21}}\times 10 \\
 & =1.2046\times {{10}^{22}}protons. \\
\end{align}\]

(b) - Now we have to calculate the mass of $1.2046\times {{10}^{22}}$ protons.
- The mass of one proton = $1.6726\times {{10}^{-27}}Kg$ .
- Therefore the mass of $1.2046\times {{10}^{22}}$ protons
\[\begin{align}
  & =(1.6726\times {{10}^{-27}}Kg)(1.2044\times {{10}^{22}}) \\
 & =2.0145\times {{10}^{-5}}Kg \\
\end{align}\]
- Finally the number of protons and the mass of the protons are not going to change with temperature and pressure.

Note: There is no effect of temperature and pressure on the number of protons and mass of the protons in any molecule. Number of protons and mass of the protons are independent of the temperature and pressure present.