Which equation will you use to calculate the volume of a 5.00-liter sample of air at 50°C when it is warmed to 100°C at constant pressure?
(V1/T1) = (V2/T2)
Thank You, DrBob222.
To calculate the volume of the air sample when it is warmed from 50°C to 100°C at constant pressure, you will need to use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, as long as the pressure remains constant.
The equation for Charles's Law is:
V1 / T1 = V2 / T2
Where:
V1 = initial volume of the gas (in liters)
T1 = initial temperature of the gas (in Kelvin)
V2 = final volume of the gas (in liters)
T2 = final temperature of the gas (in Kelvin)
In this case, you are given the initial volume as 5.00 liters and the initial temperature as 50°C. To convert the temperature to Kelvin, you need to add 273.15 to the initial temperature:
T1 = 50°C + 273.15 = 323.15 K
The final temperature is given as 100°C. Again, convert this temperature to Kelvin:
T2 = 100°C + 273.15 = 373.15 K
Now, substitute the values into the Charles's Law equation:
5.00 L / 323.15 K = V2 / 373.15 K
Now, you can solve for V2 by cross-multiplying:
V2 = (5.00 L * 373.15 K) / 323.15 K
V2 ≈ 5.775 L
Therefore, the volume of the 5.00-liter sample of air at 50°C when it is warmed to 100°C at constant pressure is approximately 5.775 liters.
To calculate the volume of a gas sample undergoing a temperature change at constant pressure, we can use the equation known as Gay-Lussac's law.
Gay-Lussac's law states that the volume of a gas is directly proportional to its absolute temperature if the pressure is kept constant. The equation is given as:
V₁/T₁ = V₂/T₂
where V₁ and T₁ are the initial volume and temperature of the gas, and V₂ and T₂ are the final volume and temperature of the gas.
In this case, you are given the initial volume (5.00 liters) and the initial temperature (50°C), and you want to calculate the final volume when the temperature is increased to 100°C.
First, convert the temperatures to the Kelvin scale by adding 273.15 to each value:
T₁ = 50°C + 273.15 = 323.15 K
T₂ = 100°C + 273.15 = 373.15 K
Now, substitute the given values into Gay-Lussac's law:
V₁/T₁ = V₂/T₂
5.00 L / 323.15 K = V₂ / 373.15 K
To find V₂, rearrange the equation and solve for V₂:
V₂ = (5.00 L / 323.15 K) * 373.15 K
Calculate the result, and round it to the appropriate number of significant figures based on the given values.