Respuesta :
Answer:
184.62 ml
Explanation:
Let [tex]p_1, v_1,[/tex] and [tex]T_1[/tex] be the initial and [tex]p_2, v_2,[/tex] and [tex]T_2[/tex] be the final pressure, volume, and temperature of the gas respectively.
Given that the pressure remains constant, so
[tex]p_1=p_2[/tex] ...(i)
[tex]v_1[/tex] = 200 ml
[tex]T_1= 26 ^{\circ}C = 273+26 =299[/tex] K
[tex]T_2= 3 ^{\circ}C = 273+3 =276[/tex] K
From the ideal gas equation, pv=mRT
Where p is the pressure, v is the volume, T is the temperature in Kelvin, m is the mass of air in kg, R is the specific gas constant.
For the initial condition,
[tex]p_1v_1=mRT_1 \\\\mR= \frac{p_1v_1}{T_1}\cdots(ii)[/tex]
For the final condition,
[tex]p_2v_2=mRT_2 \\\\mR= \frac{p_2v_2}{T_2}\cdots(iii)[/tex]
Equating equation (i), and (ii)
[tex]\frac{p_1v_1}{T_1}=\frac{p_2v_2}{T_2}[/tex]
[tex]\frac{v_1}{T_1}=\frac{v_2}{T_2}[/tex] [from equation (i)]
[tex]v_2=\frac{T_2}{T_1} \times v_1[/tex]
Putting all the given values, we have
[tex]v_2=\frac{276}{299} \times 200 = 184.62 \; ml[/tex]
Hence, the volume of the gas at 3 degrees Celsius is 184.62 ml.
