2012 AL Physics PAPER IIA, Q37

用戶31980

2012-09-09 3:47 am

The desities of steam and water (both at 100 degree celcius and under 1atm) are 0.61kgm-3 and 1000kgm-3 respectively. Find the approximate ratio of average separation of steam molecules to that of water molecules under such conditions.

回答 (1)

天同

2012-09-09 8:23 am

✔ 最佳答案

1 mole of water/steam contains molecules equal to one Avogadro's number Na (which is 6.02 x 10^23), and the molar mass of water/steam is 18 g/mol

Given density of steam = 0.61 kg/m^2 = 6.1x10^-4 g/cm^3
Consider 1 cm^3 of steam, mass of steam molecules = 6.1x10^-4 g
hence, no. of molecules present = (6.1x10^-4/18)Na
Separation between steam molecules = cube-root[ (18/6.1x10^-4)Na] cm

Similar for water, given density of water = 1000 kg/m^2 = 1 g/cm^3
Consider 1 cm^3 of water, mass of water molecules = 1 g
hence, no. of molecules present = (18/1)Na
Separation between water molecules = cube-root[(18/1)Na] cm

Hence, ratio = cube-root[( (18/6.1x10^-4)Na)/([(18/1)Na)]
= cube-root[1/6.1x10^-4] cm = 11.79

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