In Unit 1, we told about how Avogadro said that equal volumes of gases at the same temperature and pressure contain the same number of particles. Mathematically, this is represented as V = an, where V = volume, n = number of moles, and a = a proportionality constant. Basically, this equation means that for a gas at constant temperature and pressure the volume is directly propotional to the number of moles of gas.
Suppose we have a sample of oxygen gas, that is 15 L in volume and contains .75 moles of gas. If all of the oxygen is converted to ozone, at constant temperature and pressure, what will be the volume of the ozone?
The balanced equation for the reaction is:
3 O2 + 2 O3. To calculate the moles of ozone produced, we must use the mole ratio, 2 mol O3 / 3 mol O2. We started out with .75 moles of O2, so we multiply it by the mole ratio:
.75 mol O2 x 2 mol O3/3 mol O2 = .5 mol O3
Avogadro's law can be rearranged so that V/n = a. Since a is constant, the equation can be rewritten as:
V1 / n1 = V2/n2.
V1 = 15 L, n1 = .75 mol, n2 = .5 mol, and you must solve for V2. Plugging in the numbers, (15 L) / (.75 mol) = (V2) / (.5 mol), and V2 = 10 L.
So far, we have learned of three laws that describe the behavior of gases. They are Boyle's Law, Charles's Law, and Avogadro's law. These relationships show how volume of a gas depends on pressure, temperature, and number of moles present. They can be combined, represented by the equation V = R([Tn]/P), where R is the combined proportionality constant called the universal gas constant. When pressure is in atmospheres and volume is in liters, R has the value of 0.08206 L atm/K mol. The above equation can also be rearranged to what is known as the ideal gas law, PV = nRT. When using this equation, remember to convert pressure to atmospheres, volume to liters, temperature to kelvins, and amount present to moles.
A sample of oxygen gas has a volume of 4.52 liters at a temperature of 10 C and a pressure of 1.5 atm. Calculate the number of moles of oxygen gas present in this sample.
The ideal gas law can be rearranged to solve for n (number of moles), n = PV/RT. In this problem, P = 1.5 atm, V = 4.52 L, T = 10 C + 273 = 283 K, and R = .08206 L atm/K mol. Plugging in your numbers, you have n = (1.5 atm)(4.52 L)/(.08206 L atm/K mol)(283 K) = .292 moles.
A sample of hydrogen gas has a pressure of 345 torr at a temperature of -10 C and a volume of 4.33 L. If conditions are changed so that the temperature is 26 C and the pressure is 468 torr, what will be the new volume?
Since the pressure, temperature, and volume all change while the number of moles remains constant, we rearrange the ideal gas law to PV/T = nR. Since nR will be the same before and after the change, we can say that:
P1 V1 / T1 = P2 V2 / T2.
We are solving for V2, so we rearrange this to the form:
V2 = T2 P1 V1 / T1 P2. P1 = 345 torr, T1 = -10 C + 273 = 263 K, V1 = 4.33 L, T2 = 26 C + 273 = 299 K, P2 = 468 torr, and we have to solve for V2. Plugging in the numbers, V2 = (299 K)(345 torr)(4.33 L)/(263 K)(468 torr) = 3.63 liters.
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Unit 2 - Section 5
Unit 2 - Section 7