Question

For the reaction 148O → 147N + ?, if 106.1 g of oxygen reacts, what volume (in L) of nitrogen gas (N₂) is produced at 273 K and 1.00 atm?

(The isotopic mass of 148O is 14.008596 amu, and the isotopic mass of 147N is 14.003074 amu.)

Answer 1

To find the volume of nitrogen gas produced, use the molar ratios of the balanced equation. Given 106.1 g of oxygen, calculate the number of moles of oxygen. Use the ideal gas law to find the volume of nitrogen gas.

Step-by-step explanation:

To find the volume of nitrogen gas produced, we need to use the molar ratios of the balanced equation. From the equation 148O → 147N + ?, we can see that for every 1 mole of oxygen, 1 mole of nitrogen gas is produced.

First, we need to calculate the number of moles of oxygen using its given mass and molar mass. Using the isotopic mass of 148O (14.008596 amu), we can convert grams to moles:

(106.1 g) / (14.008596 g/mol) = 7.57 mol

Since the molar ratio between oxygen and nitrogen is 1:1, we know that 7.57 moles of oxygen will produce an equal number of moles of nitrogen gas. Now we can use the ideal gas law to find the volume of nitrogen gas. Rearranging the ideal gas law equation and plugging in the given values:

V = (nRT) / P

V = (7.57 mol)(0.0821 L.atm.mol⁻¹.K⁻¹)(273 K) / 1.00 atm = 173.39 L