A sample of gas occupies 4 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
(P1V1/T1) = (P2V2/T2)
K i have to agree with the DrBob222, but one thing I do different is
P1V1T2 = P2V2T1 instead of the division.
GIT GUD BOB
To find the pressure at which the gas sample would occupy 500 mL at a temperature of 525ºC, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure
V = Volume
n = Number of moles
R = Ideal gas constant
T = Temperature
First, we need to convert the temperature from Celsius to Kelvin:
T(K) = T(ºC) + 273.15
T(K) = 525 + 273.15 = 798.15 K
Next, we need to find the number of moles of the gas sample. We can assume the number of moles remains constant (since the gas is not reacting), so we can use the following equation based on the constant volume:
n1 / T1 = n2 / T2
Where:
n1 = initial number of moles
T1 = initial temperature
n2 = final number of moles
T2 = final temperature
Since we have STP conditions at the start (Standard Temperature and Pressure), we know that at STP, 1 mole of gas occupies 22.4 L. By using this information, we can find the initial number of moles:
4 mL = 4 / 1000 = 0.004 L (converting mL to L)
0.004 L / 22.4 L/mol = 1.79 x 10^-4 moles
Now we can use the equation to find the final number of moles:
n1 / T1 = n2 / T2
1.79 x 10^-4 moles / 273.15 K = n2 / 798.15 K
Solving for n2:
n2 = (1.79 x 10^-4 moles * 798.15 K) / 273.15 K
n2 = 5.22 x 10^-4 moles
Now we have the final number of moles, we can calculate the pressure at the final volume using the ideal gas law equation:
P1V1 / T1 = P2V2 / T2
Where:
P1 = initial pressure (STP conditions, 1 atm)
V1 = initial volume (4 mL = 0.004 L)
T1 = initial temperature (273.15 K)
P2 = final pressure (unknown)
V2 = final volume (500 mL = 0.5 L)
T2 = final temperature (798.15 K)
1 atm * 0.004 L / 273.15 K = P2 * 0.5 L / 798.15 K
Solving for P2:
P2 = (1 atm * 0.5 L * 273.15 K) / (0.004 L * 798.15 K)
P2 = 85.677 atm
Finally, converting the pressure to torr:
1 atm = 760 torr
85.677 atm * 760 torr/atm = 65085.72 torr
Therefore, the pressure at which the gas sample would occupy 500 mL at a temperature of 525ºC is approximately 65085.72 torr.
To find the pressure at which the gas sample would occupy 500 mL at a temperature of 525ºC, we can use the ideal gas law equation:
PV = nRT
Where:
P is the pressure (in units of torr)
V is the volume (in mL)
n is the number of moles of gas
R is the ideal gas constant (0.0821 L·atm/mol·K)
T is the temperature (in Kelvin)
First, we need to convert the temperature from Celsius to Kelvin.
T(K) = T(ºC) + 273.15
T(K) = 525ºC + 273.15 = 798.15 K
Next, we need to determine the number of moles of gas present in the initial and final conditions. To do this, we can use the relationship:
n1/V1 = n2/V2
where n1 and n2 represent the number of moles in the initial and final states, and V1 and V2 represent the volumes in the initial and final states.
In the initial state:
V1 = 4 mL
In the final state:
V2 = 500 mL
Since the amount of gas remains constant, we can write:
n1/V1 = n2/V2
Solving for n2:
n2 = (n1)(V2/V1)
Now, let's substitute the values into the equation:
n2 = (n1)(V2/V1)
n2 = (n1)(500 mL / 4 mL)
n2 = 125(n1)
So, in the final state, we have 125 times the number of moles of gas compared to the initial state.
Now, we can rearrange the ideal gas law equation and isolate the pressure (P):
P = (n2)(R)(T) / V2
Substituting the values into the equation, we get:
P = (125n1)(0.0821 L·atm/mol·K)(798.15 K) / 500 mL
To simplify the calculation, we need to convert mL to liters:
V2 = 500 mL = 0.5 L
Now, let's substitute the values and calculate the pressure:
P = (125n1)(0.0821 L·atm/mol·K)(798.15 K) / 0.5 L
To find the value of n1, we need additional information about the gas. If the gas is given, you can determine its molar mass and use the given volume to calculate the number of moles.
Once you have the value of n1, substitute it into the equation above and calculate the pressure (P) in units of torr.