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Answer 1 · 2017-07-15T13:59:38

#"gas added" = 11.9# #"mol"#

To solve this, we can use the quantity-volume relationship of gases.

According to Avogadro's hypothesis:

The number of moles of a gas is directly to proportional to the volume the gas occupies.

And, under constant temperature and pressure conditions, we get the equation

#(V_1)/(n_1) = (V_2)/(n_2)# (constant temperature and pressure)

Our known quantities are:

We can plug these into the equation and solve for the final quantity, #n_2#:

#n_2 = (n_1V_2)/(V_1) = ((9.51color(white)(l))(18.3cancel("L")))/(8.15cancel("L")) = color(red)(21.4# #color(red)("mol"#

We're asked to find the number of moles needed to be added: so we subtract the initial amount from the final amount:

#"gas added" = color(red)(21.4# #color(red)("mol"# #- 9.51# #"mol"# #= color(blue)(11.9# #color(blue)("mol"#