Given a gas is at 21 Land 9 mol, what is the volume of the gas when the number of moles changes to 8 mol? Round to one decimal place. square

To solve this problem, we can use the ideal gas law equation:<br /><br />PV = nRT<br /><br />Where:<br />- P is the pressure of the gas<br />- V is the volume of the gas<br />- n is the number of moles of the gas<br />- R is the universal gas constant<br />- T is the absolute temperature of the gas<br /><br />- Initial number of moles (n1) = 21 L<br />- Final number of moles (n2) = 8 mol<br /><br />We need to find the final volume (V2) of the gas when the number of moles changes to 8 mol.<br /><br />Using the ideal gas law equation, we can write:<br /><br />P1V1 = n1RT<br />P2V2 = n2RT<br /><br />Since the pressure and temperature remain constant, we can equate the two equations:<br /><br />P1V1 = P2V2<br /><br />Substituting the given values:<br /><br />P1 × 21 L = P2 × V2<br /><br />To find the final volume (V2), we can rearrange the equation:<br /><br />V2 = (P1 × 21 L) / P2<br /><br />Since the pressure (P1 and P2) is the same, we can simplify the equation:<br /><br />V2 = 21 L × n2)<br /><br />Substituting the given values:<br /><br />V2 = 21 L × (21 L / 8 L)<br />V2 = 56.25 L<br /><br />Rounding the answer to one decimal place, the final volume of the gas when the number of moles changes to 8 mol is 56.3 L.