A sample of gas occupies 8 mL at STP. At
what pressure would this sample occupy 500
mL if the temperature is changed to 525◦C?
Answer in units of torr.
To find the pressure at which the sample of gas would occupy 500 mL at a temperature of 525°C, we can use the combined gas law. The combined gas law equation is:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
Where:
P1 = initial pressure (STP pressure)
V1 = initial volume (8 mL)
T1 = initial temperature (STP temperature, 0°C or 273 K)
P2 = final pressure (to be determined)
V2 = final volume (500 mL)
T2 = final temperature (525°C or 798 K)
Let's plug in the values into the equation and solve for P2:
(P1 * V1) / (T1) = (P2 * V2) / (T2)
(1 atm * 8 mL) / (273 K) = (P2 * 500 mL) / (798 K)
1 * 8 / 273 = P2 * 500 / 798
0.0292 = P2 * 0.6266
P2 = 0.0292 / 0.6266
P2 ≈ 0.0467 atm
To convert atm to torr, we multiply by 760:
Pressure in torr = P2 * 760
Pressure in torr ≈ 0.0467 * 760
Pressure in torr ≈ 35.47 torr
Therefore, the sample of gas would occupy 500 mL at a pressure of approximately 35.47 torr when the temperature is changed to 525°C.
To solve this problem, we can use the ideal gas law equation, which is given by:
PV = nRT
Where:
P = Pressure of the gas
V = Volume of the gas
n = Number of moles of the gas
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature in Kelvin
First, we need to convert the initial volume to liters because all the other units are in liters. 8 mL is equal to 0.008 L.
Next, since this is an STP (Standard Temperature and Pressure) problem, we know that the temperature is 273 K.
Now we have the initial volume (V1) = 0.008 L, the final volume (V2) = 0.5 L, the initial temperature (T1) = 273 K, and the final temperature (T2) = 525°C.
Since the temperature is in Celsius, we need to convert it to Kelvin:
T2 = 525 + 273 = 798 K
We can now set up the equation using the given values:
(P1 * V1) / T1 = (P2 * V2) / T2
Substituting the known values, we get:
(P1 * 0.008) / 273 = (P2 * 0.5) / 798
Cross-multiplying, we have:
(P1 * 0.008 * 798) = (P2 * 0.5 * 273)
Now we can solve for P2:
P2 = (P1 * 0.008 * 798) / (0.5 * 273)
To find the pressure in units of torr, we can use the conversion factor:
1 atm = 760 torr
Finally, we can substitute the given value of P1:
P2 = (1 atm * 0.008 * 798) / (0.5 * 273) * 760 torr
Calculating this expression will give us the answer in torr.
Use (P1V1/T1) = (P2V2/T2)
Remember T must be in kelvin.