Answer:
56.9 mL
Explanation:
To solve this problem, we can use the equation of state for an ideal gas, which states that:
[tex]pV=nRT[/tex]
where
p is the pressure of the gas
V is its volume
n is the number of moles in the gas
R is the gas constant
T is the absolute temperature of the gas
For a gas undergoing a transformation, n and R remain constant, so we can rewrite the equation as:
[tex]\frac{p_1 V_1}{T_1}=\frac{p_2 V_2}{T_2}[/tex]
where in this case:
[tex]p_1 = 690 mmHg = 0.908 atm[/tex] is the initial pressure of the gas
[tex]V_1=75 mL[/tex] is the initial volume
[tex]T_1=-45^{\circ}+273=228 K[/tex] is the initial temperature of the gas
[tex]p_2 = 1 atm[/tex] is the final pressure (at STP)
[tex]T_2 = 273 K[/tex] is the final temperature (at STP)
Solving for V2, we find the final volume of the gas:
[tex]V_2=\frac{p_1 V_1T_2}{T_1p_2}=\frac{(0.908)(75)(228)}{(273)(1)}=56.9 mL[/tex]
