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Answer 1 · 2017-07-15T13:59:38

$gas added = 11.9$ $"gas added" = 11.9$ $mol$ $"mol"$

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

$\frac{V_{1}}{n_{1}} = \frac{V_{2}}{n_{2}}$ $(V_1)/(n_1) = (V_2)/(n_2)$ (constant temperature and pressure)

Our known quantities are:

We can plug these into the equation and solve for the final quantity, $n_{2}$ $n_2$ :

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

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

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