Answer:
The volume of the gas at standard temperature and pressure is 378 mL.
Step-by-step Explanation:
To solve this problem, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas:
P1V1/T1 = P2V2/T2
where P1, V1, and T1 are the initial pressure, volume, and temperature, respectively, and P2, V2, and T2 are the final pressure, volume, and temperature, respectively.
We know that the gas has an initial pressure of 100 mmHg and an initial volume of 480 mL at a temperature of 40°C. We want to find the final volume of the gas at standard temperature and pressure, which is defined as 0°C and 1 atm (or 760 mmHg) of pressure.
First, we need to convert the initial temperature from Celsius to Kelvin by adding 273.15:
T1 = 40°C + 273.15 = 313.15 K
Next, we can plug in the values into the combined gas law equation:
(100 mmHg)(480 mL)/(313.15 K) = (760 mmHg)(V2)/(273.15 K)
We can solve for V2 by cross-multiplying and simplifying:
V2 = (100 mmHg)(480 mL)(273.15 K)/(313.15 K)(760 mmHg)
= 378 mL
Therefore, the volume of the gas at standard temperature and pressure is 378 mL.