Answer :
The partial pressure of nitrogen is 0.63 atm if the gaseous mixture exerts a total pressure of 0.90 atmospheres.
The mole fraction of nitrogen is given to be 7 moles. We can calculate the partial pressure of nitrogen by using the equation given by Raoult's law;
partial pressure of nitrogen = total pressure × mole fraction of nitrogen
As the total moles of the gaseous mixture given is;
7 + 2.5 + 0.5 = 10 moles
We first determine the number of moles of nitrogen in one mole of the mixture as follows;
7 moles of nitrogen = 10 moles of gaseous mixture
x moles of nitrogen = 1 mole of gaseous mixture
x = 7 ÷ 10 = 0.7 moles
Hence 0.7 moles of nitrogen are present in 1 mole of the gaseous mixture. Now the partial pressure of nitrogen can be calculated as follows;
partial pressure of nitrogen = 0.9 × 0.7
partial pressure of nitrogen = 0.63 atm
Therefore, the partial pressure of nitrogen is calculated to be 0.63 atm.
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