Step-by-step explanation:
We have to inflate a baggie and we know the volume, the pressure, and the temperature of the gas. The formula that relates all these measures is the ideal gas law.
P * V = n * R * T
Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas contant (0.082 atm*L/mol*K) and T is the temperature.
Before we plug the values in the formula we have to convert the volume from mL to L.
1000 mL = 1 L
V = 816 mL * 1 L/(1000 mL) = 0.816 L
V = 0.816 L
P = 0.847 atm
T = 303 K
We can use the given values and solve the formula for the number of moles.
P * V = n * R * T
n = P * V/(R * T)
n = 0.847 atm * 0.816 L/(0.082 atm*L/(mol*K) * 303 K)
n = 0.0278 moles
Now we can convert those 0.0278 moles of N₂ into grams using the molar mass of N₂.
molar mass of N = 14.00 g/mol
molar mass of N₂ = 2 * 14.00 g/mol
molar mass of N₂ = 28.00 g/mol
mass of N₂ = 0.0278 moles * 28.00 g/mol
mass of N₂ = 0.778 g
Answer: 0.778 g of nitrogen are needed.