Question

Consider thermal decomposition of ammonium dichromate:
${\left( {{\text{N}}{{\text{H}}_4}} \right)_2}{\text{C}}{{\text{r}}_2}{{\text{O}}_7}\xrightarrow{{{\text{Heat}}}}{\text{C}}{{\text{r}}_2}{{\text{O}}_3} + 4{{\text{H}}_2}{\text{O}} + {{\text{N}}_2}$
Calculate:
A.The volume of nitrogen at STP evolved when 63 g of ammonium dichromate is heated.
B.The mass of ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$ formed at the same time
$\left[ {{\text{Atomic mass: }} {\text{N}} = 14,{\text{H}} = 1,{\text{Cr}} = 52,{\text{O}} = 16} \right]$.

Answer 1

From the balanced chemical equation we will get to know the value of substance formed per mole of the reactant. Using a unitary method we will calculate the mass. The volume at STP for 1 mol is $22.4{\text{ L}}$.

Complete step by step answer:
The balanced chemical equation for the decomposition of ammonium dichromate is:
${\left( {{\text{N}}{{\text{H}}_4}} \right)_2}{\text{C}}{{\text{r}}_2}{{\text{O}}_7}\xrightarrow{{{\text{Heat}}}}{\text{C}}{{\text{r}}_2}{{\text{O}}_3} + 4{{\text{H}}_2}{\text{O}} + {{\text{N}}_2}$
As it is clear from the equation that 1 mole of ammonium dichromate is required to produce 1 mole of nitrogen gas.
The molar mass is calculated by adding the atomic mass of each element multiplied by the respective atoms used.
The molar mass of ammonium dichromate that is ${\left( {{\text{N}}{{\text{H}}_4}} \right)_2}{\text{C}}{{\text{r}}_2}{{\text{O}}_7}$ is equal to $\left( {14 \times 4} \right) \times 2 + 2 \times 52 + 7 \times 16 = 252$.
The volume of one mole of substance at standard condition of temperature and pressure is $22.4{\text{ L}}$.
One mole of ammonium dichromate or 252 gram of ammonium dichromate will produce $22.4{\text{ L}}$ of nitrogen gas. Using unitary method,
The volume of nitrogen produced from 63 g of ammonium dichromate will be:
$\dfrac{{22.4}}{{252}} \times {\text{63}} = 5.6{\text{ L}}$
The molar mass of ${\text{C}}{{\text{r}}_2}{{\text{O}}_3}$ will be: $2 \times 52 + 3 \times 16 = 152$
As we know that 1 mole of ammonium dichromate will produce one mole of chromium oxide that means that 256 g of ammonium dichromate will produce 152 gram of chromium oxide. We need to calculate for 63 grams of ammonium dichromate. So again using the unitary method we will get the mass of chromium oxide formed as:
$\dfrac{{152}}{{252}} \times {\text{63}} = 38{\text{ g}}$

Hence, the volume of nitrogen produced is $5.6{\text{ L}}$ and the mass of chromium oxide formed is 38 g.

Note:
STP stands for standard condition for temperature and pressure. The value of temperature at STP is $273.15{\text{ K}}$ and pressure equals 1 bar. Decomposition reactions are those reactions in which one substance decomposes to form one or more than one compounds.