PROBLEM 72P

A sample of gas has a mass of 0.555 g. Its volume is 117 mL at a temperature of 85 °C and a pressure of 753 mm Hg. Find the molar mass of the gas.

Solution 72P

Given that

Mass =0.555g

Volume =117 mL.

Temperature= 85oC.

Pressure =753 mmHg.

We know that

With the ideal gas equation PV=nRT

Explanation:

Boyle's law, published in 1662, established a relationship between gas pressure and volume. Say you have a gas in a cylinder, and then you make the volume twice as big by pulling on a piston. The pressure is reduced by half. This is called an inverse relationship.

Charles law, discovered in 1801, determined that if you keep the pressure constant, the volume of a gas is directly proportional to its temperature. However, you must use the Kelvin temperature scale that starts at absolute zero, -273.15 degrees Celsius.

Avogadro's law states that there an equal number of gas atoms or molecules in a given volume of gas. And he invented the concept of the mole, which is defined as the number of atoms in 12 grams of Carbon 12. This is 6.02x1023. What they determined is that one mole of gas will occupy exactly 22.4 litres at standard temperature (0C or 273.15K) and pressure (760 mmHg or 1 atmosphere).

Put them all together, with the constant R, which is dependant on what units you are using, and n, the number of moles, and you can plug into the equation.

The value of R we will use in this case is 0.0821 L atm/mole K

In this case, because you are looking for n, you need to restate the equation by dividing both sides by RT. Now you have n=PV/RT.

pv=nrt

n=pv/rt

n=[(753/760)(.117)/[(.08206 Latm/molK)(...

r = ideal gas constant, and that is .08206 for these units

t = kelvin always, so 85C +273 = K

p = atmospheres, 753/760 = atm

v = liters, .117

n = .00395 moles

.555g/.00395 moles = 140.65 or 141 g/mol with 3 significant figures