O Stas of Matter Using the ideal equation of state A reaction at \( -10.0^{\circ} \mathrm{C} \) evolves \( 490 . \mathrm{mmol} \) of dinitrogen difluoride gas. Calculate the volume of dinitrogen difluoride gas that is collected. You can assume the pressure in the room is exactly 1 atm. Round your answer to 3 significant digits.

To calculate the volume of dinitrogen difluoride gas collected, we can use the ideal gas equation: \[ PV = nRT \] where: - \( P \) is the pressure in atmospheres (atm), - \( V \) is the volume in liters (L), - \( n \) is the number of moles of gas, - \( R \) is the gas constant (\( 0.08206 \, \text{L atm/mol K} \)), - \( T \) is the temperature in Kelvin (K). Given: - Pressure (\( P \)) = 1 atm - Number of moles (\( n \)) = \( 490 \, \text{mmol} = 0.49 \, \text{mol} \) (converting mmol to mol) - Temperature (\( T \)) = \( -10.0^{\circ} \text{C} = 263.15 \, \text{K} \) (converting Celsius to Kelvin) We can rearrange the ideal gas equation to solve for volume (\( V \)): \[ V = \frac{nRT}{P} \] Substitute the given values into the equation to find the volume of dinitrogen difluoride gas collected. Calculate the value by following steps: - step0: Calculate: \(\frac{\left(0.49\times 0.08206\times 263.15\right)}{1}\) - step1: Remove the parentheses: \(\frac{0.49\times 0.08206\times 263.15}{1}\) - step2: Multiply the terms: \(10.58110361\) The volume of dinitrogen difluoride gas collected is approximately \( 10.581 \, \text{L} \) when rounded to 3 significant digits.