At what temperature will a mass of a gas occupying 200cm3 at 0°C have a volume of 300cm3 if the pressure remains constant?
Use V1/T1 = V2/T2. Remember T must be in kelvin.
K = 273.15 + degrees celsius
To find the temperature at which the gas will have a volume of 300 cm³, we can use Charles' Law, which states that the volume of a gas is directly proportional to its temperature if the pressure is held constant.
The equation for Charles' Law is:
V₁ / T₁ = V₂ / T₂
Where:
V₁ is the initial volume of the gas (200 cm³)
T₁ is the initial temperature of the gas (0°C or 273.15K)
V₂ is the final volume of the gas (300 cm³)
T₂ is the final temperature of the gas (unknown)
Rearranging the equation to solve for T₂:
T₂ = (V₂ * T₁) / V₁
Plugging in the given values:
T₂ = (300 cm³ * 273.15K) / 200 cm³
Simplifying:
T₂ = 409.725K
Therefore, at a temperature of approximately 409.73K, or 136.58°C, the gas will have a volume of 300 cm³ if the pressure remains constant.
To calculate the temperature at which a gas occupies a different volume while the pressure remains constant, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure of the gas (constant)
V is the volume of the gas (initial and final)
n is the number of moles of gas
R is the ideal gas constant
T is the temperature in Kelvin
In this case, we have the initial volume (V1) as 200 cm3, and the final volume (V2) as 300 cm3. The pressure (P) remains constant, but we are not given the value, so we do not need it for our calculation.
First, we need to convert the initial and final volumes from cm3 to liters since the ideal gas constant (R) is usually expressed in liters.
1 cm3 = 1/1000 liter
Initial volume (V1) = 200 cm3 = 200/1000 = 0.2 L
Final volume (V2) = 300 cm3 = 300/1000 = 0.3 L
We can rearrange the ideal gas law equation to solve for temperature (T):
T = (PV) / (nR)
Since the pressure (P), number of moles (n), and gas constant (R) are constant, we can write the equation as:
T1 / V1 = T2 / V2
Now, we can substitute the known values into the equation:
T1 / 0.2 = T2 / 0.3
To find T2 (the final temperature):
T2 = (T1 * 0.3) / 0.2
However, we still need to convert the temperature from Celsius to Kelvin since the ideal gas law uses Kelvin scale.
To convert from Celsius to Kelvin: K = °C + 273.15
Assuming the initial temperature (T1) is given in Celsius, you need to convert it to Kelvin.
Once you have the value of T1 in Kelvin, you can substitute it into the equation:
T2 = ((T1 + 273.15) * 0.3) / 0.2
This will give you the final temperature T2 in Kelvin.