Potassium hypobromite, KOBr, converts ammonia to nitrogen by the following reaction.
3KOBr + 2NH3 N2 + 3KBr + 3H2O
To prepare 448.2 mL of dry N2, when measured at 22.3 °C and 777.3 torr, what is the minimum number of grams of KOBr required?
To find the minimum number of grams of KOBr required to produce 448.2 mL of dry N2, we need to use the stoichiometry of the balanced equation and the ideal gas law.
Step 1: Calculate the number of moles of N2
Using the ideal gas law, we can convert the volume of N2 to the number of moles. The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atm) = 777.3 torr = 777.3/760 atm
V = volume (in liters) = 448.2 mL = 448.2/1000 L
n = number of moles
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature (in Kelvin) = 22.3 °C + 273.15 = 295.45 K
Rearranging the ideal gas law equation to solve for n, we have:
n = PV / RT
Substituting the given values:
n = (777.3/760) * (448.2/1000) / (0.0821 * 295.45)
Calculate the numerical value of n.
Step 2: Determine the stoichiometry of the reaction
From the balanced equation, we see that 3 moles of KOBr react to produce 1 mole of N2. This gives us the stoichiometric ratio:
3 moles KOBr : 1 mole N2
Step 3: Calculate the moles of KOBr required
Since the stoichiometric ratio is 3:1, the number of moles of KOBr required can be found by multiplying the number of moles of N2 (calculated in step 1) by the ratio:
moles KOBr = n (from step 1) * (3 moles KOBr / 1 mole N2)
Calculate the numerical value of the moles of KOBr required.
Step 4: Convert moles of KOBr to grams
Use the molar mass of KOBr to convert moles to grams. The molar mass of KOBr is the sum of the atomic masses of each element in the molecule:
Molar mass of KOBr = (atomic mass of K) + (atomic mass of O) + (atomic mass of Br)
Look up the atomic masses of K, O, and Br, and calculate the molar mass.
grams KOBr = moles KOBr * molar mass of KOBr
Calculate the numerical value of the grams of KOBr required.
The final numerical value of the grams of KOBr required will depend on the specific values calculated in each step.