The atomic mass of potassium is 19 g/mol
90.0 g of potassium contains ;
= 90.0/19
= 4.737 moles
The reaction between potassium and nitrogen is given by the equation;
6K + N2 = 2K3N
The mole ratio of potassium and nitrogen is 6:1
The number of moles of nitrogen;
= 4.737/6
= 0.7895 moles
But, 1 mole of nitrogen occupies 22.4 liters at STP
Therefore; 0.7895 moles × 22.4 liters
= 17.685 liters
