An aqueous solution of ammonium nitrite decomposes when heated to give off nitogen gas and water. This reaction can be used to prepare pure nitrogen gas. How many grams of ammonium nitrite must have reacted if 3.75 liters of nitrogen gas was colleced over water at 25˚C and 97.8 kPa? I keep getting 11.8 g but my teacher said its wrong because of it being over water. Can someone show me the steps to get the correct answer? thanks.
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To solve this problem, we need to use the ideal gas law and the concept of partial pressure.
Step 1: Convert the given conditions to the proper unit.
The volume of nitrogen gas is given as 3.75 liters. However, since the gas was collected over water, we need to account for the vapor pressure of water at 25˚C, which is 2.8 kPa. Therefore, the total pressure is 97.8 kPa - 2.8 kPa = 95.0 kPa.
Step 2: Convert the volume of gas to the number of moles.
We can use the ideal gas law equation, PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.
In this case, we have P = 95.0 kPa, V = 3.75 liters, and T = 25°C + 273.15 = 298.15 K.
To convert pressure to atm and volume to liters, divide the values by 101.3 (since 1 atm = 101.3 kPa).
So, P = 95.0 kPa / 101.3 kPa/atm = 0.937 atm
V = 3.75 L
Using the ideal gas law, we can calculate the number of moles (n):
n = PV / RT
Using R = 0.0821 L·atm/(mol·K), we have:
n = (0.937 atm) * (3.75 L) / (0.0821 L·atm/(mol·K) * 298.15 K)
Solving this equation will give you the number of moles of nitrogen gas produced.
Step 3: Convert moles of nitrogen gas to moles of ammonium nitrite.
From the balanced chemical equation, we know that 1 mol of ammonium nitrite produces 1 mol of nitrogen gas. Therefore, the number of moles of ammonium nitrite is equal to the number of moles of nitrogen gas.
Step 4: Convert moles of ammonium nitrite to grams.
The molar mass of ammonium nitrite (NH4NO2) can be calculated by adding up the atomic masses of its elements: (1 x atomic mass of N) + (4 x atomic mass of H) + (2 x atomic mass of O).
Once you have the molar mass, you can multiply the number of moles of ammonium nitrite by the molar mass to obtain the mass in grams.
Using these steps, you should be able to accurately calculate the number of grams of ammonium nitrite that reacted.