Calculation based on number of molecules — lesson. Science State Board, Class 10.

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1.	Calculate the number of molecules in \(11.2\) \(L\) of \(CO_2\) at STP.

Data:

Given volume of \(CO_2=11.2\) \(L\)

Molar volume of \(CO_2=22.4\) \(L\)

Avogadro's number \(=6.023\times10^{23}\)

Solution:

\begin{array}{l} Number of moles of {CO}_{2} & = & \frac{Volume at STP}{Molar volume} \\ = & \frac{11.2}{22.4} \\ = & 0.5 mole \end{array}

\begin{array}{l} Number of molecules of {CO}_{2} & = & Number of moles of {CO}_{2} \times Avogadro number \\ = & 0.5 \times 6.023 \times 10^{23} \\ = & 3.011 \times 10^{23} molecules \end{array}

Therefore, the number of molecules in \(11.2\) \(L\) of \(CO_2\) at STP \(=3.011\times10^{23}\)

2.	Calculate the number of molecules in \(54\) \(g\) of \(H_2O\).

Data:

Given mass of \(H_2O=54\) \(g\)

Gram molecular mass of \(H_2O=18\) \(g\)

Avogadro's number \(=6.023\times10^{23}\)

Solution:

\begin{array}{l} Number of molecules = \frac{Avogadro number \times Given mass}{Gram molecular mass} \\ \begin{array}{l} Number of molecules of water & = & 6.023 \times 10^{23} \times \frac{54}{18} \\ = & 18.069 \times 10^{23} \end{array} \end{array}

Therefore, the number of molecules in \(54\) \(g\) of \(H_2O=18.069\times10^{23}\) \(molecules\)

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10. Calculation based on number of molecules