The volume at stp occuppied by a gas Q originally occupying 153.7dm at 287k and 750mm pressure (vapor pressure of gas Q at 287k is 12mm of Hg)
To find the volume of gas Q at STP (Standard Temperature and Pressure), 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 gas constant, and T is the temperature.
First, let's convert the given volume from dm³ to liters:
153.7 dm³ = 153.7 L
Next, convert the pressure from mmHg to atmospheres (atm):
1 atm = 760 mmHg
750 mmHg = 750/760 atm = 0.9868 atm
Given:
Volume (V) = 153.7 L
Pressure (P) = 0.9868 atm
Temperature (T) = 287 K
We need to calculate the number of moles (n) of gas Q. To do this, we rearrange the ideal gas law equation to solve for n:
n = (PV) / (RT)
Now we substitute the given values into the equation:
n = (0.9868 atm * 153.7 L) / (0.0821 L•atm/mol•K * 287 K)
n = 12.42 mol
We have determined that the number of moles (n) of gas Q is 12.42 mol.
Now, to find the volume at STP, we can use the relationship between moles and volume for gases at STP:
1 mole of any gas occupies 22.4 L at STP
Therefore, the volume of gas Q at STP can be calculated by multiplying the number of moles by the molar volume:
Volume at STP = number of moles * molar volume
= 12.42 mol * 22.4 L/mol
Volume at STP = 277.5688 L
Hence, the volume occupied by gas Q at STP is approximately 277.57 L.