A sample of nitrogen gas has the temperature drop from 250°C to 150°C at constant pressure. What is the final volume if the initial volume is 310 mL?
V1/V2=T1/T2
temps in Kelvins
To find the final volume of the nitrogen gas, we can use the ideal gas law equation: 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 using the equation K = °C + 273.15:
Initial temperature (T1) = 250°C + 273.15 = 523.15 K
Final temperature (T2) = 150°C + 273.15 = 423.15 K
Since the pressure is constant, we can cancel it out from the equation, leaving us with:
V1/T1 = V2/T2
Now let's plug in the values we have:
V1 = 310 mL = 0.310 L
T1 = 523.15 K
T2 = 423.15 K
Putting all these values into the equation, we can solve for V2 (the final volume):
0.310 L / 523.15 K = V2 / 423.15 K
To solve for V2, we cross-multiply and solve for V2:
V2 = (0.310 L * 423.15 K) / 523.15 K
V2 ≈ 0.250 L
Therefore, the final volume of the nitrogen gas is approximately 0.250 L.
To solve this problem, we can use the ideal gas law, which states that the product of pressure (P), volume (V), and temperature (T) of an ideal gas is constant. The equation for the ideal gas law is:
PV = nRT
Where:
P = pressure of the gas
V = volume of the gas
n = number of moles of the gas
R = ideal gas constant
T = temperature of the gas
In this problem, the pressure is constant, so we can simplify the equation to:
V/T = constant
To find the final volume, we can use the equation above and the initial and final temperatures:
V1 / T1 = V2 / T2
Let's plug in the values:
V1 = 310 mL = 310 cm^3 (convert from mL to cm^3)
T1 = 250°C = 523.15 K (convert from °C to Kelvin)
T2 = 150°C = 423.15 K (convert from °C to Kelvin)
V2 = (V1 * T2) / T1
V2 = (310 cm^3 * 423.15 K) / 523.15 K
Calculating the result:
V2 = 251.266 cm^3
Therefore, the final volume of the nitrogen gas is approximately 251.266 cm^3.