Question

250 cm³ of ammonia gas is at 27° C. Find its volume at the following temperatures, when pressure remains constant.

Normal temperature

Answer 1

Step-1: Understand the given conditions

• Pressure is constant.
• Volume of Ammonia $\left({\mathrm{NH}}_3\right)$= $250{\mathrm{cm}}^3$
• Temperature of Ammonia= $27°\mathrm{C}$
• Volume to be calculated at normal temperature
• The value of normal temperature is taken as $273\mathrm{K}$

Step-2: Perform unit conversion from degree Celsius to Kelvin

The relationship of degree Celsius and Kelvin is as shown below

$\mathrm{Temperature}\mathrm{in}°\mathrm{C}+273=\mathrm{Temperature}\mathrm{in}\mathrm{K}$

Conversion of $27°\mathrm{C}$ to K

• $27+273=300\mathrm{K}$

Step-3: Apply Charles' law equation to find out the volume at the given normal temperature i.e.; $273\mathrm{K}$

Charles' law: According to Charles' law, at constant pressure, volume is directly proportional to temperature for a given mass of the gas.
or $\frac{\mathrm{V}}{\mathrm{T}}=\mathrm{constant}$

Therefore, for two different conditions i.e. 1 and 2, Charles' law can be written as:
$\frac{{\mathrm{V}}_1}{{\mathrm{T}}_1}=\frac{{\mathrm{V}}_2}{{\mathrm{T}}_2}$

• Let volume of Ammonia at temperature $300\mathrm{K}$= ${\mathrm{V}}_1$i.e.; $250{\mathrm{cm}}^3$
• Let temperature of Ammonia at volume ${\mathrm{V}}_1$= ${\mathrm{T}}_1$i.e.; $300\mathrm{K}$
• Let temperature of Ammonia at volume ${\mathrm{V}}_2$= ${\mathrm{T}}_2$ i.e.; $273\mathrm{K}$
• Let volume of Ammonia at temperature ${\mathrm{T}}_2$= ${\mathrm{V}}_2$ (to be calculated)

Substituting the values in the above equation

$$\begin{gathered} \frac{250}{300}=\frac{{\mathrm{V}}_2}{273} \\ {\mathrm{V}}_2=\frac{250\times 273}{300} \\ {\mathrm{V}}_2=\frac{68250}{300}=227.5{\mathrm{cm}}^3 \end{gathered}$$

${\mathrm{V}}_2=227.5{\mathrm{cm}}^3$