Question

Calculate molar volume of an ideal gas in m^3 at room temperature and pressure (or RTP). Id other words, calculate how much volume one mole of an ideal gas at 1.01 times 10^5 Pa and 298 K takes up. Then convert it to liters (l), where 1 t - 0.001 m^3 Measured at 18.00 C, a lead rod has a length of 52.44 cm, and an iron rod has a length of 52.61 cm. Both rods are heated to 86.0 C. After heating, which rod is longer, and by how much? Remember that you calculate the change in length, and then add that change to the original length. The question is whether the extra increase in length in the lead carry 4 significant figures for this calculation. The coefficient of linear expansion for lead is alpha = 28.9 mu m/(m middot K), and for iron, 11.8 mu m/(m middot K), where 1 micron = 1 mu m = 10^-6 m.

Answer 1

1)

This idea came from Avogadro's Hypothesis which was re-examined by Cannizzaro in 1858. The hypothesis states that "Equal volumes of different gases under the same temperature and pressure contain equal number of molecules".

At normal temperature and pressure,

(mass of one litre of any gas/mass of one litre of hydrogen)

= (mass of one litre of any gas)/0.09 [considering mass of one litre H2 gas as 0.09 g]

= Relative Density (D) of any gas.

Thus, mass of one litre of any gas = 0.09 X D.

Again, relative density of any gas = (mass of one molecule of the gas)/(mass of one molecule of H2)

= (Molecular mass of the gas, M)/2.016.

Therefore,

Mass of 1 litre of any gas at N.T.P. = 0.09 X (M/2.016) .

0.09 X (M/2.016) grams occupy 1 litre at N.T.P.

M gram or one mole of any gas occupies (2.016/0.09) litre or 22.4 litres.