States of Matter

Question

The compressibility factor for a real gas at high pressure is

$1 plus RT over pb$
$1$
$1 plus pb over RT$
$1 minus pb over RT$

Answer

1 plus pb over RT

Vander Waal's equation for one mole of real gas is
$open parentheses straight p plus straight a over straight V squared close parentheses space left parenthesis straight v minus straight b right parenthesis space equals space RT When space pressure space is space high space straight p space greater than greater than straight a over straight V squared such space that space open parentheses straight p space plus straight a over straight V squared close parentheses space equals space straight p thus comma space straight p left parenthesis straight v minus straight b right parenthesis space equals space RT pV minus pb space equals space RT pv space equals space RT space plus pb therefore space COmpressibillity space factor comma straight z space equals space pV over RT space equals space open parentheses 1 plus pb over RT close parentheses$