The car stopped due to a gravitational pull (gravity slowing it down) the energy is converted to kinetic energy and heat energy.
We know that:
number of moles (n) = mass / molar mass
Now, from the general law of gases:
PV = nRT
where:
P is the pressure = 500 torr = 0.65 atm
V is the volume
n is the number of moles
R is the gas constant = 0.082
T is the temperature = 300 k
We will just rearrange this equation as follows:
P = nRT / V
Then we will substitute n with its equivalent equation mentioned at the beginning:
P = (mass x R x T) / (volume x molar mass) ......> equation I
Now, we know that:
density = mass / volume
We will substitute (mass/volume) in equation I with density as follows:
P = (density x R x T) / molar mass
Rearrange this equation to get the mass as follows:
molar mass = <span>dRT/P = (0.216 x 0.082 x 300) / 0.65 = 8.4738 grams
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From the periodic table:
molecular mass of hydrogen = 1 grams
molecular mass of nitrogen = 14 grams
Therefore:
molar mass of hydrogen = 2 x 1 = 2 grams
molar mass of nitrogen = 2 x 14 = 28 grams
We can assume that the number of moles of of each element is y.
We can thus build up the following equation:
2y + 28y = 8.4738
30y = 8.4738
y = 0.28246
Therefore:
mole fraction of hydrogen = 2 x 0.28246 = 0.56492
mole fraction of nitrogen = 28 x 0.28246 = 7.90888
Using ideal gas equation,
PV=nRT
Where P=pressure(atm), V=volume(L), n=number of moles of the gas, R=gas constant, 0.0821 atm L/moles K, T=temperature(K)
At STP:
P=1 atm
T=273K
n=1 as given
So using ideal gas equation,
V=nRT/P
So,
V=1*0.0821*273/1
=22.4 L
This would be a synthesis reaction
