Question

If 4.40 l l of co2 c o 2 gas at 16 ∘c ∘ c at 791 mmhg m m h g is used, what is the final volume, in liters, of the gas at 39 ∘c ∘ c and a pressure of 745 mmhg m m h g , if the amount of co2 c o 2 remains the same

a) 4.19 L
b) 4.40 L
c) 5.27 L
d) 5.68 L

Answer 1

Using the Combined Gas Law, the final volume of CO2 gas at 39 °C and a pressure of 745 mmHg, when starting with 4.40 L at 16 °C and 791 mmHg, is approximately 5.17 L which is closest to option (c) 5.27 L.

Step-by-step explanation:

To calculate the final volume of CO2 gas when changing conditions from an initial state to a final state, while keeping the amount of gas constant, we can use the Combined Gas Law which is derived from the Ideal Gas Law. The formula is: (P1 × V1) / T1 = (P2 × V2) / T2 where P1 and P2 are the initial and final pressures, V1 and V2 are the initial and final volumes, and T1 and T2 are the initial and final temperatures in Kelvin.

The initial conditions are: Volume (V1) = 4.40 L, Temperature (T1) = 16 °C (which is 289.15 K) and Pressure (P1) = 791 mmHg. The final conditions are: Pressure (P2) = 745 mmHg and Temperature (T2) = 39 °C (which is 312.15 K). To find the final volume (V2), we rearrange the formula to solve for V2:

V2 = (P1 × V1 × T2) / (P2 × T1)

Plugging in the values we get:

V2 = (791 mmHg × 4.40 L × 312.15 K) / (745 mmHg × 289.15 K)

V2 = (1114204.4 mmHg·L·K) / (215579.925 mmHg·K)

V2 ≈ 5.17 L

So the final volume of the CO2 gas is approximately 5.17 liters, which is closest to 5.27 L in the list of options provided (c).