Answer to Question #302785 in Mechanical Engineering for jmmmmm

Question

Find the final weight, volume and pressure of the gas. 

Answer 1

The key tool here is the ideal gas law:

PV=nRT

Where P is pressure, V is volume, T is temperature, n is number of moles and R is a constant equal to:

R=0.0821 [L*atm/(mol*K)]

the units are liter atmospheres per mol per degree kelvin, so we will need to convert our temperature from Celsius to kelvin by adding 273 to it.

To find the number of moles we just rearrange:

n=PV/(RT) = 0.095 * 5.00 [L* atm] / (0.0821*(21+273) [K*L*atm/(mol*K)]

number of molecules = 0.019679 [mol]

To find the mass in grams we need to know how many grams a mol of SO2 weighs. Conveniently, the number of molecules in a mol was chosen specifically to make this conversion easy. First we find the number of atomic mass units within one molecule of SO2, then we simply take that to be the number of grams in a mol of SO2. Atomic mass units are the mass of a proton, or neutron, which is where basically all the mass for atoms and molecules comes from. Thus we consult the periodic table to see how many protons and neutrons are present in one molecule of SO2. S has an atomic weight of 32.065 while each oxygen contributes 15.999. roughly then we get 64 atomic mass units per molecule, which implies:

SO2 has a molecular mass of of 64 [grams/mol].

Therefore the mass of the sample is:

mass = 0.019679 [mol] * 64 [grams/mol]. = 1.259 grams