What volume of ammonia gas, measured at mmHg and 43.5 degrees C, is required to produce 8.41g of ammonium sulfate according to the following balanced chemical equation: 2NH3(g)+H2SO4(aq)->(NH4)2SO4(s)
Use the same process as in the KMnO4/Na2C2O4 problem to find mols.
Then use PV = nRT, plug in the conditions listed in the problem and solve for V
To find the volume of ammonia gas required, we need to use the ideal gas law equation:
PV = nRT
where:
P is the pressure of the gas (in this case, measured in mmHg),
V is the volume of the gas (which we need to find),
n is the number of moles of the gas,
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
and T is the temperature of the gas (in this case, measured in Kelvin).
First, let's convert the given temperature of 43.5 degrees Celsius to Kelvin.
T(K) = T(°C) + 273.15
T(K) = 43.5 + 273.15
T(K) = 316.65 K
Now, we need to determine the number of moles of ammonia gas (NH3) used in the reaction. To do this, we'll use the given mass of ammonium sulfate (NH4)2SO4 and the molar ratio between NH3 and (NH4)2SO4 from the balanced chemical equation.
1 mole of (NH4)2SO4 = 2 moles of NH3
First, find the molar mass of ammonium sulfate ((NH4)2SO4):
(N - Nitrogen: 14.01 g/mol) * 2 + (H - Hydrogen: 1.01 g/mol) * 8 + (S - Sulfur: 32.07 g/mol) + (O - Oxygen: 16.00 g/mol) * 4 = 132.14 g/mol
Now, calculate the number of moles of (NH4)2SO4:
moles = mass / molar mass
moles = 8.41 g / 132.14 g/mol = 0.06364 moles of (NH4)2SO4
Since the balanced chemical equation shows that 2 moles of NH3 are required for every 1 mole of (NH4)2SO4, we can determine the number of moles of NH3:
moles of NH3 = 2 * 0.06364 moles = 0.12728 moles
Now, let's substitute all the known values into the ideal gas law equation to find the volume:
PV = nRT
Where:
P = the pressure of the gas = you need to provide this value since it was not given in the question.
V = the volume of the gas (which we need to find)
n = the number of moles of the gas = 0.12728 moles (as calculated above)
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = the temperature of the gas = 316.65 K (as calculated above)
Solving for V, we get:
V = nRT / P
Now plug in the known values and solve for V.