Question

Calculate the number of particles in each of the following statements given in the options.
A.$46\,g$ of $Na$ atom (number from mass)
B.$8g\,{O_2}$ molecules (number of the molecules form the mass)
C.$0.1$ mole of carbon atom (number form gives moles)
D.$0.5$ mole of carbon atom (number form gives moles)

Answer 1

Hint: We know that one mole of any substance comprises $6.022 \times {10^{23}}$ particles. We can call the value of $6.022 \times {10^{23}}$ as Avogadro number (or) Avogadro constant and is represented by the symbol ${N_A}.$ We can calculate the number of particles by the moles of the substance and Avogadro number.
Formula used: We can write the formula to calculate the number of particles as,
$N = n \times {N_A}$
Here, n=number of particles in the substance
     N=mass of the substance in moles (mol)
${N_A} = $Avogadro’s number

Complete step by step answer:
A)
Given data contains $46\,g$ of $Na$ atom (number from mass). We have to calculate the number of particles in $46\,g$ of $Na$ atom (number from mass).
We have to convert mass in grams to mass in moles. From the values of calculated moles, we can multiply the moles with Avogadro’s number to obtain the number of particles. We can find out the mass in moles from mass in grams using the molar mass.
We can calculate the moles using the formula,
${\text{Moles = }}\dfrac{{{\text{Given}}\,{\text{mass}}\,{\text{(in}}\,{\text{grams)}}}}{{{\text{Molar}}\,{\text{mass}}}}$
We have to substitute the values of mass (in grams) and the molar mass.
Molar mass of sodium=$23\,g/mol$.
The given mass of sodium is $46\,g$.
We can calculate the moles as,
Amount (in moles)=$\dfrac{{46\,g}}{{23\,g/mol}}$
Amount (in moles)=$2\,mole$
So now, we can calculate the number of particles in $46\,g$ of $Na$ atom using the formula,
$N = n \times {N_A}$
Here, n=$2\,mole$ and ${N_A} = 6.023 \times {10^{23}}$
We can substitute the values of number of moles and Avogadro’s number as,
$
  N = n \times {N_A} \\
  N = 2 \times 6.023 \times {10^{23}} \\
  N = 12.046 \times {10^{23}} \\
 $
$\therefore $ The number of particles present in $46\,g$ of $Na$ atom is $12.046 \times {10^{23}}$.
B)
Given data contains $8g\,{O_2}$ molecules (number of the molecules form the mass). We have to calculate the number of particles in $8g\,{O_2}$ molecules (number of the molecules form the mass).
We have to convert mass in grams to mass in moles. From the values of calculated moles, we can multiply the moles with Avogadro’s number to obtain the number of particles. We can find out the mass in moles from mass in grams using the molar mass.
We can calculate the moles using the formula,
${\text{Moles = }}\dfrac{{{\text{Given}}\,{\text{mass}}\,{\text{(in}}\,{\text{grams)}}}}{{{\text{Molar}}\,{\text{mass}}}}$
We have to substitute the values of mass (in grams) and the molar mass.
Molar mass of oxygen=$32\,g/mol$
The given mass of oxygen is$8\,g$.
We can calculate the moles as,
Amount (in moles)=$\dfrac{{8\,g}}{{32\,g/mol}}$
Amount (in moles)=$0.25\,mole$
So now, we can calculate the number of particles in $8g\,{O_2}$ molecules using the formula,
$N = n \times {N_A}$
Here, n=$0.25\,mole$ and ${N_A} = 6.023 \times {10^{23}}$
We can substitute the values of number of moles and Avogadro’s number as,
$
  N = n \times {N_A} \\
  N = 0.25\,mole \times 6.023 \times {10^{23}} \\
  N = 1.50575 \times {10^{23}} \\
 $
$\therefore $ The number of particles present in $8g\,{O_2}$ molecules atom is $1.50575 \times {10^{23}}$.
C)
Given data contains $0.1$ mole of carbon atom (number form gives moles). We have to calculate the number of particles in $0.1$ mole of carbon atom (number form gives moles).
We can multiply the moles with Avogadro’s number to obtain the number of particles using the formula,
$N = n \times {N_A}$
Here, n=$0.1\,mole$ and ${N_A} = 6.023 \times {10^{23}}$
We can substitute the values of number of moles and Avogadro’s number as,
$
  N = n \times {N_A} \\
  N = 0.1\,mole \times 6.023 \times {10^{23}} \\
  N = 0.6023 \times {10^{23}} \\
  N = 6.023 \times {10^{22}} \\
 $
$\therefore $ The number of particles present in $0.1$ mole of carbon atom is $6.023 \times {10^{22}}$.
D)
Given data contains $0.5$ mole of carbon atom (number form gives moles). We have to calculate the number of particles in $0.5$ mole of carbon atom (number form gives moles).
We can multiply the moles with Avogadro’s number to obtain the number of particles using the formula,
$N = n \times {N_A}$
Here, n=$0.5\,mole$ and ${N_A} = 6.023 \times {10^{23}}$
We can substitute the values of number of moles and Avogadro’s number as,
$
  N = n \times {N_A} \\
  N = 0.5\,mole \times 6.023 \times {10^{23}} \\
  N = 3.0115 \times {10^{23}} \\
 $
$\therefore $ The number of particles present in $0.5$ mole of carbon atom is $3.0115 \times {10^{23}}$.

Note:
The number of constituent particles such as molecules, atoms or ions present in a sample is related with mass of the substance in the sample using the proportionality factor called as Avogadro constant/Avogadro number. The SI of Avogadro number is reciprocal mole $\left( {{\text{mol}}{{\text{e}}^{{\text{ - 1}}}}} \right)$. We know that the Avogadro number is dimensionless. We can also relate the molar volume of a substance to the average volume occupied by one of the particles, when the units of volume are in the same quantity using Avogadro constant/number.