The volume of the gas at STP is approximately 341.3 cm^3.
To find the volume of the gas at STP, we can use the ideal gas law:
PV = nRT
where:
P is the pressure
V is the volume
n is the number of moles
R is the ideal gas constant (approximately 8.314 J/mol*K)
T is the temperature in Kelvin
We can rearrange the equation to solve for the volume at STP:
V2 = V1 * T2 * P1 / (T1 * P2)
where:
V1 is the initial volume (380 cm^3)
T1 is the initial temperature (27°C + 273.15 K = 300.15 K)
P1 is the initial pressure (750 mmHg)
V2 is the final volume (unknown)
T2 is the STP temperature (0°C + 273.15 K = 273.15 K)
P2 is the STP pressure (760 mmHg)
Converting the units:
V1 = 380 cm^3 * (1 L / 1000 cm^3) = 0.38 L
P1 = 750 mmHg * (1 atm / 760 mmHg) = 0.987 atm
Plugging the values into the equation:
V2 = 0.38 L * 273.15 K * 0.987 atm / (300.15 K * 0.987 atm)
V2 ≈ 0.341 L ≈ 341.3 cm^3