Answer
Verified
430.2k+ views
Hint: The number of moles is obtained by dividing mass of the substance by molar or molecular mass and the number of molecules is calculated by multiplying moles and Avogadro’s number. Then we’ll calculate the ratio of their molecules.
Complete Step by step answer: A mole is defined as the amount of a substance which constitutes different elementary particles like atoms, molecules or ions equal to Avogadro’s number i.e., $6.022 \times {10^{22}}$ . Avogadro’s number is defined as the number of atoms present in 12 g of C-12 isotope. A molar mass of a chemical compound is defined as the mass of a part of that compound divided by the amount of substance or number of moles in it. Let the molar mass of methane be ${m_1}$, molar mass of sulphur dioxide be ${m_2}$, number of moles of methane be ${n_1}$ and number of moles of sulphur dioxide be ${n_2}$.
Now, we’ll calculate molar mass of methane $\left( {C{H_4}} \right)$ i.e.,${m_1} = 1 \times C + 4 \times H$
${m_1} = 1 \times 12 + 4 \times 1$ as molar or molecular mass of carbon is 12g and hydrogen is 1g.
$\Rightarrow {m_1} = 12 + 4$
$\Rightarrow {m_1} = 16g$
Molar mass of sulphur dioxide $\left( {S{O_2}} \right)i.e.,{m_2} = 1 \times S + 2 \times O$
${m_2} = 1 \times 32 + 2 \times 16$ as molar mass of sulphur is 32g and oxygen is 16g.
$\Rightarrow {m_2} = 32 + 32$
$\Rightarrow {m_2} = 64g$
${n_1} = \dfrac{{mass{\text{ }}of{\text{ }}methane}}{{{m_1}}}$
$\Rightarrow {n_1} = \dfrac{m}{{16}}$ [eqn.1]
${n_2} = \dfrac{{mass{\text{ }}of{\text{ }}sulphur{\text{ }}dioxide}}{{{m_2}}}$
$\Rightarrow {n_2} = \dfrac{m}{{64}}$ since equal masses are taken. [eqn.2]
We divide eqn.1 by 2,
$\dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{\dfrac{m}{{16}}}}{{\dfrac{m}{{64}}}}$
$\Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{64}}{{16}}$
$\Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = \dfrac{4}{1}$
$\Rightarrow \dfrac{{Number{\text{ }}of{\text{ }}molecules{\text{ }}of{\text{ }}methane}}{{Number{\text{ }}of{\text{ }}molecules{\text{ }}of{\text{ }}sulphur{\text{ }}dioxide}}$ =$\dfrac{{{n_1} \times 6.022 \times {{10}^{22}}}}{{{n_2} \times 6.022 \times {{10}^{22}}}}$
i.e. $\dfrac{{{n_1}}}{{{n_2}}} = \dfrac{4}{1}or4:1$
Therefore, option D is correct.
Note: We should remember that the number of molecules is obtained by multiplying the number of moles and Avogadro’s number. The number of moles is inversely proportional to molar mass of the compound. Thus, the another way to find the ratio of their molecule is on dividing the molar mass of sulphur dioxide by methane
Complete Step by step answer: A mole is defined as the amount of a substance which constitutes different elementary particles like atoms, molecules or ions equal to Avogadro’s number i.e., $6.022 \times {10^{22}}$ . Avogadro’s number is defined as the number of atoms present in 12 g of C-12 isotope. A molar mass of a chemical compound is defined as the mass of a part of that compound divided by the amount of substance or number of moles in it. Let the molar mass of methane be ${m_1}$, molar mass of sulphur dioxide be ${m_2}$, number of moles of methane be ${n_1}$ and number of moles of sulphur dioxide be ${n_2}$.
Now, we’ll calculate molar mass of methane $\left( {C{H_4}} \right)$ i.e.,${m_1} = 1 \times C + 4 \times H$
${m_1} = 1 \times 12 + 4 \times 1$ as molar or molecular mass of carbon is 12g and hydrogen is 1g.
$\Rightarrow {m_1} = 12 + 4$
$\Rightarrow {m_1} = 16g$
Molar mass of sulphur dioxide $\left( {S{O_2}} \right)i.e.,{m_2} = 1 \times S + 2 \times O$
${m_2} = 1 \times 32 + 2 \times 16$ as molar mass of sulphur is 32g and oxygen is 16g.
$\Rightarrow {m_2} = 32 + 32$
$\Rightarrow {m_2} = 64g$
${n_1} = \dfrac{{mass{\text{ }}of{\text{ }}methane}}{{{m_1}}}$
$\Rightarrow {n_1} = \dfrac{m}{{16}}$ [eqn.1]
${n_2} = \dfrac{{mass{\text{ }}of{\text{ }}sulphur{\text{ }}dioxide}}{{{m_2}}}$
$\Rightarrow {n_2} = \dfrac{m}{{64}}$ since equal masses are taken. [eqn.2]
We divide eqn.1 by 2,
$\dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{\dfrac{m}{{16}}}}{{\dfrac{m}{{64}}}}$
$\Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = \dfrac{{64}}{{16}}$
$\Rightarrow \dfrac{{{n_1}}}{{{n_2}}} = \dfrac{4}{1}$
$\Rightarrow \dfrac{{Number{\text{ }}of{\text{ }}molecules{\text{ }}of{\text{ }}methane}}{{Number{\text{ }}of{\text{ }}molecules{\text{ }}of{\text{ }}sulphur{\text{ }}dioxide}}$ =$\dfrac{{{n_1} \times 6.022 \times {{10}^{22}}}}{{{n_2} \times 6.022 \times {{10}^{22}}}}$
i.e. $\dfrac{{{n_1}}}{{{n_2}}} = \dfrac{4}{1}or4:1$
Therefore, option D is correct.
Note: We should remember that the number of molecules is obtained by multiplying the number of moles and Avogadro’s number. The number of moles is inversely proportional to molar mass of the compound. Thus, the another way to find the ratio of their molecule is on dividing the molar mass of sulphur dioxide by methane
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Which are the Top 10 Largest Countries of the World?
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Difference Between Plant Cell and Animal Cell
Give 10 examples for herbs , shrubs , climbers , creepers
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you graph the function fx 4x class 9 maths CBSE
Write a letter to the principal requesting him to grant class 10 english CBSE