Question #70d16
1 Answer
Here's what I got.
Explanation:
For starters, the reaction you're looking at here is
#3"H"_ (2(g)) + "N"_ (2(g)) -> 2"NH"_ (3(g))#
Notice that the reactants' side contains
- three moles of hydrogen gas,
#3 xx "H"_2# - one mole of nitrogen gas,
#1 xx "N"_2#
The product's side contains
- two moles of ammonia,
#2 xx "NH"_3#
Now, let's take each cube to be equivalent to one unit of volume. You can thus say that you have
#"4 moles of gas in 4 cubes " -># for the reactants' side
#"2 moles of gas in 2 cubes " -># for the product's side
Notice that the ratio of moles of gas to number of cubes remains unchanged. You have
#"4 moles gas"/"4 cubes" = "1 mole/cube " -># for the reactants' side
#"2 mole gas"/"2 cubes" = "1 mole/cube "-># for the product's side
This essentially means that the pressure remains unchanged because you get the same moles of gas to volume ratio on both sides of the reaction.
PROVE THIS USING BOYLE'S LAW
To prove this, let's assume that the volume remains constant, i.e. that you end up with
Since pressure is directly proportional to the number of moles of gas when temperature and volume are kept constant, decreasing the number of moles of gas by a factor of
You can thus say that
#color(blue)(bar(ul(|color(white)(a/a)P_1/n_1 = P_2/n_2color(white)(a/a)|)))#
Here
In this case, you'd have
#P_2 = n_2/n_1 * P_1#
#P_2 = (2 color(red)(cancel(color(black)("moles"))))/(4color(red)(cancel(color(black)("moles")))) * P_1 = 1/2 * P_1#
This is the pressure on the reactant's side if you have
Now focus on the product's side alone. You keep the number of moles of gas and the temperature constant and decrease the volume from
You know from Boyle's Law that pressure and volume have an inverse relationship when the number of moles of gas and the temperature are kept constant
#color(blue)(bar(ul(|color(white)(a/a)P_"1 product" * V_"1 product" = P_"2 product" * V_"2 product"color(white)(a/a)|)))#
In this case, you'd have
#P_"2 product" = V_"1 product"/V_"2 product" * P_"1 product"#
#P_"2 product" = (4 color(red)(cancel(color(black)("cubes"))))/(2color(red)(cancel(color(black)("cubes")))) * P_"1 product"#
#P_"2 product" = 2 * P_"1 product"#
But you know that
#P_"1 product" = 1/2 * P_1#
Here
Therefore,
#P_"2 product" = P_2 = 2 * 1/2 * P_1#
#P_"2 product" = P_1#
Once again, this goes to show that the pressure remains unchanged because you decreased the number of moles of as by a factor of