Suppose that Quebec had managed to succeed from Canada and became an independent country. Just to be difficult, they decreed that they will only measure pressure in mm Hg and volume in cm3. What value for R, the ideal gas constant, would students in Quebec use when solving the ideal gas solution?
a) 7.6 x 105
b) 6.23 x 104
c) 8.14
d) 2.78
e) 0.082
The questions begs for some additional answers. For example, Quebec may MEASURE volume in cc BUT they could also USE liters for V in the equation. Same kind of question for presure. I will assume V is to be used in cc and P in mm Hg.
PV = nRT
P = 760 mm Hg
V = 22,400 cc (for 1 mol gas)
n = 1 mol
R = ??
T = 273.15
Solve for R
Check my thinking.
A 1.00 L flask containing 450 torr of H2 is connected to and mixed with a second flask with a volume of 0.500 L containing 250 torr N2. What is the final pressure of the resulting mixed gas system?
a) 250 torr
b)383 torr
c) 450 torr
d) 575 torr
e) it cannot be determined
Answered above.
To determine the ideal gas constant (R) that students in Quebec would use, we need to understand the relationship between pressure, volume, and temperature using the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
The ideal gas constant (R) is a proportionality constant that relates the pressure, volume, and temperature of an ideal gas.
The units used for pressure, volume, and temperature in the ideal gas law equation should be consistent in order to obtain correct results. In SI units, the commonly used unit for pressure is Pascal (Pa), for volume is cubic meter (m3), and for temperature is Kelvin (K).
In the given scenario, Quebec has decided to measure pressure in mm Hg (millimeters of mercury) and volume in cm3 (cubic centimeters). Therefore, we need to convert these units to the SI units before we can determine the correct value for R.
1 mm Hg = 133.322 Pa
1 cm3 = 10^-6 m3
Now we can compare the units of pressure and volume in the ideal gas law equation to the given units in Quebec:
P (mm Hg) = 133.322 × P (Pa)
V (cm3) = 10^-6 × V (m3)
Substituting the converted units into the ideal gas law equation, we get:
(133.322 × P) × (10^-6 × V) = n × R × T
By rearranging the equation, we find:
PV = n × (R × 133.322 × 10^-6) × T
Comparing the rearranged equation to the original ideal gas law equation (PV = nRT), we can see that the constant (R × 133.322 × 10^-6) is the new value that needs to be used for R in the Quebec scenario.
Now, let's evaluate the options provided:
a) 7.6 x 105: This value does not match the factor of (R × 133.322 × 10^-6) required for conversion.
b) 6.23 x 104: This value also does not match the required conversion factor.
c) 8.14: This value is the correct value for R in the SI unit system.
d) 2.78: This value does not match the required conversion factor.
e) 0.082: This value is the value for R in the SI unit system when pressure is measured in Pa and volume is measured in m3.
Therefore, the answer is c) 8.14, which corresponds to the value for R that students in Quebec would use in the given scenario.