25 dm3 of ammonia at 283 K are heated until its volume is 30 dm3. To what temperature must it have been
raised to accomplish the change?
Answers
Answer:
Explanation:
The Ideal Gas Law
Of the three phases of matter, gases tend to exist at relatively high temperatures and low pressures. Decrease the temperature enough and the gas will condense into a liquid or sublime into a solid. Likewise, increase the pressure enough and condensation or sublimation will happen. Gases are different from solids and liquids (which are referred to as "condensed matter") in that there is room between the molecules. Typically, the space between molecules in the gas phase is large compared with the size of the molecules.
Consider a sample of gas inside a piston cylinder (a cylinder with one movable end cap so the volume inside the piston can be changed). The gas evenly fills the volume of the cylinder (the defining property of gases). If the piston is held at a fixed position, then the gas sample has the following important properties:
V = volume = the amount of space occupied by the gas, usually measured in liters (L).
P = pressure = the force per unit area exerted by the gas on its container, usually measured in atmospheres (atm) or Torricelli (torr) = mmHg. 1 atm = 760 torr = 760 mmHg.
n = number of moles, measured in moles (recall 1 mole = 6.022x1023 molecules), abbreviated mol.
T = temperature, usually measured in degrees Kelvin, abbreviated K. 273 K = 0oC, and the size of 1 degree K is the same as the size of 1 degree C.
For the purposes of this discussion we will limit ourselves to measuring pressures in atmospheres. Later, we'll do some calculations with torr. There are many other pressure units in use, particularly pounds force per square inch (psi) and Pascal = Newton per meter squared.
For most gases at temperatures near (or above) room temperature (298 K = 25o C) and near (or below) room pressure (1 atm = 760 torr), the ideal gas law adequately describes the behavior of the gas:
Where R = 0.08206 L atm mol-1K-1 is a constant of nature called the ideal gas constant.
Example (standard temperature and pressure)
What is the volume (in L) of 1 mole of an ideal gas at standard temperature (273 K) and pressure (1 atm)?
Solution
Solve the ideal gas law for the volume and plug in the numbers
Example (find temperature)
0.105 moles of an ideal gas occupy 5.00 L at a pressure of 0.975 atm. What is the temperature of the gas in K and oC?
Solution
Solve the ideal gas law for the temperature and plug in the numbers
Which is the answer in K. To get oC, use the formula
Note: Temperatures in K can never be negative, but temperatures in oC can.
Example (find moles)
How many moles of an ideal gas take up 35L of volume at 25oC and 1.5 atm?
Solution
First, convert oC to K, 25 oC +273 = 298 K, then solve the ideal gas law for moles and plug in the numbers
Example (find pressure)
2.39 moles of an ideal gas at 300 K occupy 29.0 L. What is the pressure?
Solution
Solve for the pressure and plug in the numbers:
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Density
Gases aren't very dense compared to solids and liquids, but they still have a density. Density is defined as mass per volume, and the relation between mass and moles of course is the molecular weight, Mw. The reader may have noticed that in the examples above, we really didn't care which ideal gas we talked about, just that it was ideal. Usually with density calculations, we need to know what gas we are talking about so we can calculate its molecular weight and thus put mass into the calculation.
Recall the molecular weight of a sample of a chemical is defined as
Where Mw is the molecular weight in grams per mole (g mol-1), m is the mass of the sample and n is the number of moles. Solving this for the mass gives
Density is usually given the symbol r? (Greek rho), so from the definition