1. A gas initially at 10 C must be changed to _____ C to triple the pressure.
2. When a student plotted ln [vapor pressure of a gas] vs. inverse Kelvin temperature, she obtained a straight line with a slope equal to -20000 K.
According to the Clausius Clapeyron equation, change in Hvap is _____ kJ/mol.
3. A student transfers a corked flask filled with air from the ice to the room temperature water bath. In the process he inadvertently pushes the cork further into the flask. The resulting pressure measurement will be ______ (higher, lower, the same)
4. true or false statements.
-Molecular motion is negligible at absolute zero.
-Absolute zero is the temperature when P = 0.
-When pressure is plotted on the x-axis and Celsius temperature is on the y-axis, the y-intercept is absolute zero .
To triple the pressure one must triple the temperature. The trick here is to recognize that it is the Kelvin temperature and not celsius that must be triple the original T. So 10 C = 273 + 10 = 283 K and 283 x 3 = ?? K.
OR you can do it another way.
P1/T1 = P2/T2.
Now just make up something for P1 (I suggest 1), then P2 will be 3, T1 will be 283 and you can solve for T2.
lower
esg
1. To determine the change in temperature needed to triple the pressure, we can use the ideal gas law. The ideal gas law equation is given by:
PV = nRT
Where:
- P is the pressure of the gas
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant
- T is the temperature in Kelvin
To triple the pressure, we need to find the new temperature (T2) at which the new pressure (P2) is three times the initial pressure (P1).
P2 = 3 * P1
We can then set up the ratio of the two ideal gas law equations to solve for T2:
(P2 * V) / (n * R * T2) = (P1 * V) / (n * R * T1)
Given that the volume, number of moles, and ideal gas constant remain constant, we can simplify the equation to:
P2 / T2 = P1 / T1
Substituting the values, we have:
3 * P1 / T2 = P1 / T1
Simplifying further:
3 / T2 = 1 / T1
Cross-multiplying:
3 * T1 = T2
Therefore, the gas must be changed to 3 times the initial temperature (30 °C) to triple the pressure.
2. The Clausius Clapeyron equation relates vapor pressure to changes in enthalpy of vaporization (ΔHvap) with temperature. The equation is:
ln(P2/P1) = -ΔHvap/R * (1/T2 - 1/T1)
Where:
- P2 and P1 are the vapor pressures at temperatures T2 and T1 respectively,
- ΔHvap is the change in enthalpy of vaporization,
- R is the gas constant, and
- T2 and T1 are the absolute temperatures in Kelvin.
From the given information, we have the slope of the ln(P) vs. 1/T graph as -20000 K. The slope of a straight line on such a graph is equal to -ΔHvap/R, where R is the ideal gas constant in J/(mol·K).
Since -ΔHvap/R = -20000 K, we can rearrange the equation to solve for ΔHvap:
ΔHvap = R * (-20000 K)
Substituting the value of the ideal gas constant R (which is approximately 8.314 J/(mol·K)), we can calculate the value of ΔHvap in kJ/mol.
3. When the student inadvertently pushes the cork further into the flask, thereby reducing the volume of the air inside the flask, the resulting pressure measurement will be higher. According to Boyle's law, which states that the volume of a given amount of gas at constant temperature is inversely proportional to the pressure, when the volume decreases, the pressure must increase.
4. - False. Molecular motion is not negligible at absolute zero. While molecular motion slows down significantly as temperature approaches absolute zero, it does not completely cease. According to the third law of thermodynamics, all molecular motion approaches but never reaches absolute zero.
- True. Absolute zero is defined as the temperature at which the pressure of an ideal gas becomes zero. At this temperature, molecular motion ceases, and the volume of the gas reaches its minimum. However, it is important to note that absolute zero cannot be reached in practice.
- True. According to the ideal gas law (PV = nRT), when pressure is plotted on the x-axis and temperature is plotted on the y-axis, the graph will be a straight line passing through the origin. The y-intercept of this graph represents the temperature at which the volume of the gas theoretically becomes zero, which is absolute zero.