A sample of gas occupies 17 mL at -112C. What volume does the sample occupy at 70C?
V1/T1 = V2/T2
Don't forget to change T to Kelvin. C + 273 = Kelvin
To solve this problem, we can use the combined gas law formula:
(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
T1 and T2 are the initial and final temperatures
We are given:
V1 = 17 mL
T1 = -112°C = (273.15 - 112) K = 161.15 K
T2 = 70°C = (273.15 + 70) K = 343.15 K
Now, we need to find V2.
First, rearrange the formula to solve for V2:
V2 = (P1 * V1 * T2) / (P2 * T1)
Since the problem does not provide any pressures, we can assume they are constant, canceling them out:
V2 = (V1 * T2) / T1
V2 = (17 mL * 343.15 K) / 161.15 K
Now we can calculate V2:
V2 = (5818.55 mL * K) / (161.15 K)
V2 ≈ 36.07 mL
Therefore, the sample of gas will occupy approximately 36.07 mL when the temperature rises to 70°C.
To find the volume that the gas sample occupies at 70°C, we can use the combined gas law, which relates the initial and final volumes, temperatures, and pressures of a gas sample. The combined gas law is given by the formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
- P1 and P2 are the initial and final pressures of the gas sample (assuming it remains constant)
- V1 and V2 are the initial and final volumes of the gas sample
- T1 and T2 are the initial and final temperatures of the gas sample in Kelvin
First, let's convert the given temperatures to Kelvin:
- Initial temperature (T1) = -112°C + 273.15 = 161.15 K
- Final temperature (T2) = 70°C + 273.15 = 343.15 K
Now, we'll plug in the values into the combined gas law equation and solve for V2:
(P1 * V1) / T1 = (P2 * V2) / T2
Since the pressure (P) remains constant in this problem, we can cancel it out from both sides of the equation, simplifying it to:
(V1 / T1) = (V2 / T2)
Rearranging the equation to solve for V2, we have:
V2 = (V1 * T2) / T1
Now, substitute the known values into the equation:
V2 = (17 mL * 343.15 K) / 161.15 K
Calculating the value, we have:
V2 ≈ 36.18 mL
Therefore, the gas sample would occupy approximately 36.18 mL at 70°C.