Question

If the masses of ${\text{Cr}}$ and ${\text{O}}$ are in the ratio 13: 12 in ${\text{Cr}}{{\text{O}}_3}$, then the ratio of ${\text{O}}$ that combines with the same mass of ${\text{Cr}}$ in ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$ and ${\text{Cr}}{{\text{O}}_7}$ is:
A.1 : 2
B.1 : 4
C.3 : 7
D.2 : 5

Answer 1

We need to calculate the ratio of oxygen only in the compound ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$ and ${\text{Cr}}{{\text{O}}_7}$. Use the given ratio for calculating the mass in the former compound. To find mass of oxygen in ${\text{Cr}}{{\text{O}}_7}$, we will calculate the number of moles used and then the mass.
Formula used:
${\text{number of moles }} = \dfrac{{{\text{mass}}}}{{{\text{molar mass}}}}$

Complete step by step answer:
Let us first write the basic reaction of formation of ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$, from the two reactant chromium and oxygen.
${\text{4Cr(s)}} + 3{{\text{O}}_2}({\text{g}}) \to {\text{2C}}{{\text{r}}_2}{{\text{O}}_3}({\text{s}})$
It is given to us that ${\text{Cr}}$ and ${\text{O}}$ is in the ratio 13: 12 in ${\text{Cr}}{{\text{O}}_3}$ that means 13 gram of chromium combines with 12 gram of oxygen.
Also it is given to us that mass of ${\text{Cr}}$in ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$ is same as in ${\text{Cr}}{{\text{O}}_3}$. So we will take the mass of oxygen that combines here as 6 g because here chromium gets doubled. so the mass of oxygen in the above reaction is 6 g.
Now we will write the equation for the formation of ${\text{Cr}}{{\text{O}}_7}$
${\text{2Cr(s)}} + 7{{\text{O}}_2}({\text{g}}) \to {\text{2Cr}}{{\text{O}}_7}({\text{s}})$
Here mass of chromium will be 13 gram as given to us. The mole ratio in which they combine is 2 : 7 : 2. Molar mass of chromium is 52. Hence number of moles of chromium will be:
${\text{number of moles }} = \dfrac{{{\text{mass}}}}{{{\text{molar mass}}}}$
${\text{moles }} = \dfrac{{13}}{{52}} = 0.25{\text{ moles}}$
For 2 moles of chromium 7 moles of oxygen reacts. For $0.25$ moles of chromium, the amount of oxygen reacts will be:
$0.25 \times \dfrac{7}{2} = 0.875$
Molar mass of oxygen is 16, hence we get mass of oxygen using the formula: $0.875 \times 16 = 14{\text{ g}}$
The ratio of mass of oxygen in ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$ and ${\text{Cr}}{{\text{O}}_7}$ will be 6 : 14 or we can simplify as 3 : 7.

Hence, the correct answer is C.

Note:
Chromium is a transition metal that belongs to the d block. Its atomic number is 24 and group number is 6 and belongs to 3d series. Oxygen is a p block element, whose atomic number is 8 and group number is 16. It belongs to period number 2.