Answer:
The volume of the gas at given temperature is [tex]1300 cm^3[/tex]
Explanation:
[tex]P_1[/tex] = initial pressure of gas = 1 atm
[tex]T_1[/tex] = initial temperature of gas = [tex]0^oC=273.15 K[/tex]
[tex]V_1[/tex] = initial volume of gas = [tex]310 cm^3 = 310 mL = 0.310 L[/tex]
([tex]1 cm^3= 1mL[/tex] , 1 mL = 0.001 L)
[tex]P_1V_1=nRT_1[/tex]..[1]
[tex]P_2[/tex] = final pressure of gas = 2.1 atm
[tex]T_2[/tex] = final temperature of gas = [tex]2,200^oC=273+2200 K=2473.15 K[/tex]
[tex]V_2[/tex] = final volume of gas = ?
[tex]P_2V_2=nRT_2[/tex]..[2]
By dividing [1] and [2] we get combined gas equation :,
[tex]\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}[/tex]
[tex]V_2=\frac{P_1V_1\times T_2}{T_1\times P_2}[/tex]
Now put all the given values in the above equation, we get:
[tex]V_2=\frac{1 atm\times 0.310 L\times 2473.15 K}{273.15 K\times 2.1 atm}[/tex]
[tex]V_2=1.3 L=1300 mL= 1300 cm^3[/tex]
The volume of the gas at given temperature is [tex]1300 cm^3[/tex]
