To solve this problem, we can use the combined gas law equation, which relates the initial and final conditions of temperature, pressure, and volume for a given amount of gas.
The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where: P1 = Initial pressure V1 = Initial volume T1 = Initial temperature (in Kelvin) P2 = Final pressure V2 = Final volume (unknown) T2 = Final temperature (in Kelvin)
First, let's convert the initial and final temperatures to Kelvin:
Initial temperature (T1) = 21°C + 273.15 = 294.15 K Final temperature (T2) = 37°C + 273.15 = 310.15 K
The given values are: Initial pressure (P1) = 660 mmHg Initial volume (V1) = 1.83 L Final pressure (P2) = 1 ATM
Now we can rearrange the equation to solve for the final volume (V2):
V2 = (P1 * V1 * T2) / (P2 * T1)
Plugging in the values:
V2 = (660 mmHg * 1.83 L * 310.15 K) / (1 ATM * 294.15 K)
Converting mmHg to ATM: 1 mmHg = 0.00131579 ATM
V2 = (660 * 0.00131579 * 1.83 * 310.15) / (1 * 294.15) V2 ≈ 1.990 L
Therefore, the gas will occupy approximately 1.990 liters at 37°C and 1 ATM pressure.