A rigid cylinder contains a sample of gas at STP. What is the pressure of this gas after the sample is heated to 410 K?
a. 1.0 atm
b. 0.50 atm
c. 0.67 atm
d. 1.5 atm
Explain how you get the answer.
1.5 atm
To determine the pressure of the gas after heating it to 410 K, we need to 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 (0.0821 L·atm/mol·K), and T is the temperature in Kelvin.
At STP (standard temperature and pressure, which is 273 K and 1 atm), the condition is given as the initial state of the gas. Let's assume that the volume and number of moles remain constant, so we can rewrite the equation:
P1V1/T1 = P2V2/T2
P2 = (P1 x V1 x T2) / (V2 x T1)
Since the volume is constant (rigid cylinder), we can simplify the equation further:
P2 = P1 x (T2 / T1)
Plugging in the given values:
P2 = 1 atm x (410 K / 273 K)
P2 = 1.5 atm
Thus, the pressure of the gas after heating it to 410 K is d. 1.5 atm.
To find the pressure of the gas after heating, 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 of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
Since the gas sample is at STP (Standard Temperature and Pressure), we know that the pressure is 1.0 atm and the temperature is 273 K.
Using the ideal gas law, we can set up the following equation:
(1.0 atm)(V) = (n)(R)(273 K),
where V is the volume of the cylinder.
Next, we need to find the number of moles (n) of gas. To do this, we can use the ideal gas law equation again, but this time with the new temperature (410 K) and pressure (which we are trying to find).
(P)(V) = (n)(R)(T),
where P is the pressure we are trying to find.
Substituting the known values:
(P)(V) = (n)(R)(410 K).
Now, we can rearrange the equation to solve for the pressure:
P = (n)(R)(410 K) / V.
We can see that the volume (V) is the same in both equations, so it cancels out.
Therefore, the pressure of the gas after heating to 410 K is:
P = (n)(R)(410 K).
Now, let's examine the answer choices:
a. 1.0 atm: This is the initial pressure at STP, not the pressure after heating.
b. 0.50 atm: This is a possible answer since it is half the initial pressure.
c. 0.67 atm: This is a possible answer, but we need to calculate the exact value to confirm.
d. 1.5 atm: This is not a valid answer since it is greater than the initial pressure.
To calculate the exact value, we would need to know the volume and number of moles of gas in the cylinder. Without this information, we cannot determine the exact pressure. However, based on the information given, the most reasonable answer would be:
b. 0.50 atm.