150ml of a gas at 27C is heated to 77C at a constant pressure.find the new volume of the gas.
(V1/T1) = (V2/T2)
Remember T must be in kelvin.
To find the new volume of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (constant)
V = volume
n = number of moles of the gas (constant)
R = ideal gas constant (constant)
T = temperature in Kelvin
In order to use this equation, we need to convert the temperatures from Celsius to Kelvin.
Given:
Initial volume, V1 = 150 mL = 150 cm^3
Initial temperature, T1 = 27°C
Final temperature, T2 = 77°C
First, let's convert the temperatures to Kelvin:
T1 (Kelvin) = T1 (Celsius) + 273.15
T1 (Kelvin) = 27 + 273.15
T1 (Kelvin) = 300.15 K
T2 (Kelvin) = T2 (Celsius) + 273.15
T2 (Kelvin) = 77 + 273.15
T2 (Kelvin) = 350.15 K
Since the pressure is constant, let's assume it remains the same throughout the process.
Now we can use the ideal gas law to find the new volume:
(P1)(V1) / T1 = (P2)(V2) / T2
Since the pressure is constant:
(P1)(V1) / T1 = (P2)(V2) / T2
Plugging in the known values:
(Pressure cancels out)
(150 cm^3) / 300.15 K = V2 / 350.15 K
Cross-multiplying and solving for V2:
V2 = (150 cm^3) x (350.15 K) / 300.15 K
V2 ≈ 175.02 cm^3
Therefore, the new volume of the gas is approximately 175.02 cm^3.
To find the new volume of the gas, we can use the combined gas law equation:
(P1 * V1) / T1 = (P2 * V2) / T2
where:
- P1 is the initial pressure (assumed to be constant)
- V1 is the initial volume
- T1 is the initial temperature
- P2 is the final pressure (assumed to be constant)
- V2 is the final volume (which we want to find)
- T2 is the final temperature
In this case, the problem states that the pressure is constant, so we can disregard the pressure terms in the equation. Hence, the equation simplifies to:
(V1 / T1) = (V2 / T2)
Now let's plug in the given values:
- V1 = 150 ml
- T1 = 27°C + 273.15 (convert to Kelvin)
- T2 = 77°C + 273.15 (convert to Kelvin)
Substituting these values into the equation, we get:
(150 / (27 + 273.15)) = (V2 / (77 + 273.15))
Now we can solve for V2:
V2 = (150 / (27 + 273.15)) * (77 + 273.15)
Calculating the right-hand side, we find:
V2 ≈ 165.65 ml
Therefore, the new volume of the gas is approximately 165.65 ml.