A sample of gas occupies 100ml at 25 degree celsius. What volume would the gas occupy at 32 degree celsius if the pressure remains constant
(V1/T1) = (V2/T2)
To solve this problem, we can use the combined gas law formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (constant)
V1 = initial volume = 100 ml
T1 = initial temperature = 25 °C (convert to Kelvin, T1 = 25 + 273.15)
T2 = final temperature = 32 °C (convert to Kelvin, T2 = 32 + 273.15)
V2 = final volume (unknown)
First, let's convert the temperatures to Kelvin:
T1 = 25 + 273.15 = 298.15 K
T2 = 32 + 273.15 = 305.15 K
Now we can substitute these values into the formula:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Since the pressure (P1) is constant, it cancels out:
(V1) / (T1) = (V2) / (T2)
Now plug in the known values:
(100 ml) / (298.15 K) = (V2) / (305.15 K)
To find V2, cross multiply and solve for V2:
V2 = (100 ml) * (305.15 K) / (298.15 K)
V2 ≈ 102.75 ml
Therefore, the gas would occupy approximately 102.75 ml at 32 degrees Celsius if the pressure remains constant.
To solve this problem, we can use the ideal gas law, which states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the temperatures from Celsius to Kelvin.
25 degrees Celsius + 273.15 = 298.15 Kelvin
32 degrees Celsius + 273.15 = 305.15 Kelvin
Since the pressure remains constant, P1 = P2. Therefore, we can rewrite the ideal gas law equation as:
V1/T1 = V2/T2
Now, substitute the given values into the equation:
V1 = 100 ml
T1 = 298.15 K
T2 = 305.15 K
V2 = (V1 * T2) / T1
V2 = (100 ml * 305.15 K) / 298.15 K
V2 = 102.43 ml
Therefore, the gas would occupy approximately 102.43 ml at 32 degrees Celsius, assuming the pressure remains constant.