Answer
Verified
403.5k+ views
Hint- In order to deal with this question, we will use the concept as minimum molar mass means that at least one atom of Mg should be present in one molecule of the given compound. And one atom of Mg and N weight is 24 and 14g respectively, use these things to get the answer.
Complete step-by-step answer:
Given that
A compound contains $6\% $ Mg by mass
This can be considered the same as 6g of Mg in 100g of compound.
Minimum molar mass of the compound is $n \times {10^2}g/mol$
We know that
Min. molar mass means the compound will contain at least one atom of Mg.
$
6gm{\text{ of }}Mg \to 100gm{\text{ of compound}} \\
\Rightarrow 1gm{\text{ of }}Mg \to \dfrac{{100}}{6}gm{\text{ of compound}} \\
$
One atom of Mg weights 24g
$
\Rightarrow 24gm{\text{ of }}Mg \to \dfrac{{100 \times 24}}{6}gm{\text{ of compound}} \\
\Rightarrow 24gm{\text{ of }}Mg \to 400gm{\text{ of compound}} \\
$
Therefore, the minimum molar mass of the compound is $400gm/mole$
Or
\[
400gm/mole = n \times {10^2}g/mol \\
\Rightarrow 4 \times {10^2}gm/mole = n \times {10^2}g/mol \\
\Rightarrow n = 4 \\
\]
Therefore the value of n is 4.
Now for the value of m:
Given that Caffeine has a Molar weight of 194u
And has $30\% $ by mass of nitrogen
$30g$ of nitrogen in $100g$ of caffeine
\[
\Rightarrow 100gm{\text{ of Caffeine}} \to 30gm{\text{ of nitrogen}} \\
\Rightarrow 1gm{\text{ of Caffeine}} \to \dfrac{{30}}{{100}}gm{\text{ of nitrogen}} \\
\Rightarrow 194gm{\text{ of Caffeine}} \to \dfrac{{30 \times 194}}{{100}}gm{\text{ of nitrogen}} \\
\Rightarrow 194gm{\text{ of Caffeine}} \to 58.2gm{\text{ of nitrogen}} \\
\]
No. of atoms of \[{N_2}\] in one molecule of caffeine is m.
Also we know that one atom of nitrogen weighs 14g
So let us find the number of atoms in 58.2gm
\[
\Rightarrow 58.2gm{\text{ of Nitrogen}} \to \dfrac{{58.2}}{{14}}{\text{atoms of nitrogen}} \\
\Rightarrow 58.2gm{\text{ of Nitrogen}} \to 4.1{\text{atoms of nitrogen}} \\
\]
No. of atoms of \[{N_2}\] in one molecule of caffeine is \[m = 4.1\]
So, the value of m is almost equal to 4.
Further we will find the ratio $m/n$:
$
\Rightarrow \dfrac{m}{n} = \dfrac{{4.1}}{4} \approx \dfrac{1}{1} \\
\Rightarrow m:n = 1:1 \\
$
Hence, the required ratio is 1:1
So, the correct answer is option B.
Note- The molar mass is known as the mass of a sample of that compound expressed in moles, divided by the volume of material in that sample. The molar mass is a substance's weight, not its molecular structure. In order to solve such types of problems students must remember the atomic weight of some common elements and also must know how to find the atomic weight from the periodic table.
Complete step-by-step answer:
Given that
A compound contains $6\% $ Mg by mass
This can be considered the same as 6g of Mg in 100g of compound.
Minimum molar mass of the compound is $n \times {10^2}g/mol$
We know that
Min. molar mass means the compound will contain at least one atom of Mg.
$
6gm{\text{ of }}Mg \to 100gm{\text{ of compound}} \\
\Rightarrow 1gm{\text{ of }}Mg \to \dfrac{{100}}{6}gm{\text{ of compound}} \\
$
One atom of Mg weights 24g
$
\Rightarrow 24gm{\text{ of }}Mg \to \dfrac{{100 \times 24}}{6}gm{\text{ of compound}} \\
\Rightarrow 24gm{\text{ of }}Mg \to 400gm{\text{ of compound}} \\
$
Therefore, the minimum molar mass of the compound is $400gm/mole$
Or
\[
400gm/mole = n \times {10^2}g/mol \\
\Rightarrow 4 \times {10^2}gm/mole = n \times {10^2}g/mol \\
\Rightarrow n = 4 \\
\]
Therefore the value of n is 4.
Now for the value of m:
Given that Caffeine has a Molar weight of 194u
And has $30\% $ by mass of nitrogen
$30g$ of nitrogen in $100g$ of caffeine
\[
\Rightarrow 100gm{\text{ of Caffeine}} \to 30gm{\text{ of nitrogen}} \\
\Rightarrow 1gm{\text{ of Caffeine}} \to \dfrac{{30}}{{100}}gm{\text{ of nitrogen}} \\
\Rightarrow 194gm{\text{ of Caffeine}} \to \dfrac{{30 \times 194}}{{100}}gm{\text{ of nitrogen}} \\
\Rightarrow 194gm{\text{ of Caffeine}} \to 58.2gm{\text{ of nitrogen}} \\
\]
No. of atoms of \[{N_2}\] in one molecule of caffeine is m.
Also we know that one atom of nitrogen weighs 14g
So let us find the number of atoms in 58.2gm
\[
\Rightarrow 58.2gm{\text{ of Nitrogen}} \to \dfrac{{58.2}}{{14}}{\text{atoms of nitrogen}} \\
\Rightarrow 58.2gm{\text{ of Nitrogen}} \to 4.1{\text{atoms of nitrogen}} \\
\]
No. of atoms of \[{N_2}\] in one molecule of caffeine is \[m = 4.1\]
So, the value of m is almost equal to 4.
Further we will find the ratio $m/n$:
$
\Rightarrow \dfrac{m}{n} = \dfrac{{4.1}}{4} \approx \dfrac{1}{1} \\
\Rightarrow m:n = 1:1 \\
$
Hence, the required ratio is 1:1
So, the correct answer is option B.
Note- The molar mass is known as the mass of a sample of that compound expressed in moles, divided by the volume of material in that sample. The molar mass is a substance's weight, not its molecular structure. In order to solve such types of problems students must remember the atomic weight of some common elements and also must know how to find the atomic weight from the periodic table.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE