# Physical chemistry

1. In a cylinder sealed by a movable piston on one side a mole of N2 gas is mixed with a couple moles of H2 gas at appropriate conditions to cause the following reaction: 3H2(g) + N2(g) → 2NH3(g). (a) Will the cylinder’s volume increase, decrease or stay the same? (b) If the piston is not allowed to move what will happen to the pressure in the cylinder?3.(a) How high must a column of ethylene glycol (antifreeze) be to exert a pressure equal to normal atmospheric pressure? Ethylene glycol’s density is 1.113 g/ml and recall mercury’s density is 13.6 g/ml. (b) What is the shortest and tallest of the following columns of liquids formed to give 1 atm of pressure: ethyl alcohol d = 0.789 g/ml; water d = 1.00 g/ml, ethylene glycol.

1.

a) The balanced reaction equation is

3*H2(g) +N2(g) = 2*NH3(g)

From this equation one can say that from 3 moles H2 and 1 mole N2 it results 2 moles NH3.

Since in the reaction enters only 2 moles H2 and 1 mole N2 it will result less than 2 moles NH3.

Now we know that for all gases the molar volume is the same  in normal conditions (22.4 liters). this means that initial the volume will be

$Vi= (2+1)*22.4 =67.2 liter$

and the final volume will be less than Vf where

$Vf = 1*22.4 =22.4 liter$

b) If the piston is not allowed to move and the temperature inside the cylinder will remain the same then as general transformation of a gas says

$P1*V1/T1= P2*V2/T2$ (where 1 is the normal state (the sate with less volume) and 2 the final state (the sate in which the volume does not change because the piston is blocked))

the final pressure will decrease into the cylinder.

3.

a) The position pressure inside a liquid is given by definition by the

$P= \rho*g*H$ where ro is the density of the liquid and H the height of the liquid column

noting with 1 the values corresponding to ethylene glycol and with 2 the values corresponding to mercury (the normal height of mercury column for 1 atmosphere is 760 mm = 0.76 m) we have

$\rho1*H1 =\rho_2*H2$

$H1 = \rho_2*H2/\rho_1 =13.6*0.76/1.113 = 9.287 meter$

b) As said before the piston pressure is $P = \rho*g*h$ and so the higher the density of the liquid the shortest its column height .

In order from the shortest to the longest column one has 1. ethylene glycol, 2. water, 3 ethyl alcohool