91Ó°ÊÓ

By using ideal gas equation, i.e.$\mathbf{,}\mathbf{}\mathbf{pv}\mathbf{=}\mathbf{nRT}\mathbf{,}$find the number of moles of gas and the final volume occupied by the gas.

Formula is as follow:

$pv=nRT$

Where, p is pressure, v is volume, T is temperature, R is universal gas constant and n is number of moles.

Initially convert temperature in Celsius to Kelvin, i.e.,

$$\begin{gathered} T_i=10°\text{C}=273.15+10=283.15\text{‿é} \\ {T}_f=30°\text{C}=273.15+30=303.15\text{‿é} \end{gathered}$$

According to ideal gas equation,

$pv=nRT$

Assume there are no leaks. For finding the number of moles of gas, use the initial condition,

$$\begin{gathered} p_i{v}_i=nR{T}_i \\ n=\frac{p_i{v}_i}{R{T}_i} \end{gathered}$$

By putting the value,

$$\begin{gathered} n=\frac{1×{10}^5×2.5}{8.31×283.15} \\ n=0.0106×{10}^5 \\ n=106.248\text{″¾´Ç±ô}≈106\text{″¾´Ç±ô} \end{gathered}$$

Hence, the number of moles of the gas presentare$106\text{″¾´Ç±ô}$

According to ideal gas equation, find the final volume occupied by the gas,

$p_f{v}_f=nR{T}_f$

By rearranging the given equation for final temperature,

$$\begin{gathered} v_f=\frac{nR{T}_f}{p_f} \\ {v}_f=\frac{106.248×8.31×303.15}{3×{10}^5} \\ {v}_f=0.892{\text{″¾}}^3 \end{gathered}$$

Hence, if the pressure is now raised to and the temperature is raised to$\text{30°°ä}$ , then the volume occupied by the gas is$0.892{\text{″¾}}^3$ .