What are some examples of the Avogadro's law?

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What are some examples of the Avogadro's law?

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Answer 1 · 2014-12-27T14:07:46

I've got a nice example for you:

You have a $V_{i n i t i a l}$ $V_(i nitial)$ -L balloon at room temperature ( $22^{\circ} C$ $22^@C$ ) and normal pressure ( $1 a t m$ $1 atm$ ). What will the final volume of the balloon be after you remove 1/3 of the initial number of moles present in the balloon and then double the remaining number of moles in the balloon?

So, let's go about solving this using Avogadro's law; according to this, the volume a gas occupies is proportional to the number of gas molecules present in that respective volume - at constant pressure and temperature.

$\frac{V}{n} = c o n s t a n t \to \frac{V_{1}}{n_{1}} = \frac{V_{2}}{n_{2}}$ $V/n = c on st ant -> V_1/n_1 = V_2/n_2$ , this describes how volume and number of moles are related for transitions between two stages.

Let's break this problem up into two stages: after the removal of moles (1) and after the addition of moles (2). So, the initial number of moles in the balloon was $n$ $n$

$\frac{V_{i n i t i a l}}{n} = \frac{V_{1}}{\frac{2}{3} n} \to V_{1} = \frac{\frac{2}{3} n \cdot V_{i n i t i a l}}{n} = \frac{2}{3} V_{i n i t i a l}$ $V_(i nitial)/n = V_1/(2/3n) -> V_1 = (2/3n * V_(i nitial))/n = 2/3 V_(i nitial)$ - for (1)

The number of moles went from $n$ $n$ to $(n - \frac{1}{3} \cdot n) = \frac{2}{3} n$ $(n - 1/3*n) = 2/3n$ - notice that the volume decreased to match the drop in the number of moles. Now,

$\frac{V_{1}}{\frac{2}{3} n} = \frac{V_{2}}{2 \cdot \frac{2}{3} n} \to V_{2} = \frac{\frac{4}{3} n \cdot V_{1}}{\frac{2}{3} n} = 2 V_{1}$ $V_1/(2/3n) = V_2/(2 * 2/3n) -> V_2 = (4/3n * V_1)/(2/3n) = 2V_1$ - for (2)

The number of moles doubled - from $\frac{2}{3} n$ $2/3n$ to $\frac{4}{3} n$ $4/3n$ , which caused the volume to double. If we express this in terms of $V_{i n i t i a l}$ $V_(i nitial)$ and $n$ $n$ , we get

$V_{f i n a l} = V_{2} = 2 \cdot V_{1} = 2 \cdot \frac{2}{3} V_{i n i t i a l} = \frac{4}{3} V_{i n i t i a l}$ $V_(f i nal) = V_2 = 2 * V_1 = 2 * 2/3V_(i nitial) = 4/3 V_(i nitial)$ and
$n_{f i n a l} = \frac{4}{3} n$ $n_(f i nal) = 4/3n$

Again, an overall increase in the number of moles caused the volume to match this increase.

Here's a video of other Avogadro's law examples;

http://socratic.org/chemistry/the-behavior-of-gases/gas-laws/avogadros-law

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What are some examples of the Avogadro's law?

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