what volume of ammonia gas, measured at 647.5 mmHg and 36.1C is required to produce 6.53 g of ammonium sulfate according to the following. 2NH3+H2SO4-(NH4)2SO4
mols (NH4)2SO4 you want = grams/molar mass = ?
Convert mols (NH4)2SO4 to mols NH3 using the coefficients in the balanced equation.
Then convert mols NH3 volume (in L) using PV = nRT.
To solve this problem, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres (atm)
V = volume in liters (L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(K·mol))
T = temperature in Kelvin (K)
Now, let's break down the problem step by step:
Step 1: Convert the given temperature to Kelvin
The temperature is given in Celsius, so we need to convert it to Kelvin by adding 273.15.
T = 36.1 + 273.15 = 309.25 K
Step 2: Convert the pressure to atmospheres
The pressure is given in mmHg, and we need to convert it to atmospheres.
1 atm = 760 mmHg
647.5 mmHg = 647.5/760 atm ≈ 0.8526 atm
Step 3: Calculate the number of moles of ammonia gas (NH3)
We need to find the moles using the ideal gas law equation.
PV = nRT
n = PV / RT
n = (0.8526 atm)(V) / (0.0821 L·atm/(K·mol))(309.25 K)
Step 4: Calculate the number of moles of ammonium sulfate (NH4)2SO4
From the balanced equation, we know that 2 moles of NH3 produce 1 mole of (NH4)2SO4. Therefore, the number of moles of (NH4)2SO4 will be half the number of moles of NH3.
moles of (NH4)2SO4 = (0.5)(moles of NH3)
Step 5: Convert moles of (NH4)2SO4 to grams
The molar mass of (NH4)2SO4 is 132.14 g/mol.
mass of (NH4)2SO4 = (moles of (NH4)2SO4)(molar mass of (NH4)2SO4)
Step 6: Substitute the given mass of (NH4)2SO4 and solve for the volume of NH3 gas
We know that 6.53 g of (NH4)2SO4 is produced.
So, (moles of (NH4)2SO4)(molar mass of (NH4)2SO4) = 6.53 g
Now, let's calculate the volume of NH3 gas:
0.5(moles of NH3) = 6.53 g / (molar mass of (NH4)2SO4)
moles of NH3 = (6.53 g / (molar mass of (NH4)2SO4)) * 2
PV = nRT
V = (nRT) / P
Substitute the calculated moles of NH3, the given pressure (0.8526 atm), the gas constant (0.0821 L·atm/(K·mol)), and the given temperature (309.25 K) into the equation to solve for V.
V = [(moles of NH3) * (0.0821 L·atm/(K·mol)) * (309.25 K)] / (0.8526 atm)
Calculate the volume using these values. The resulting value will be the volume of ammonia gas required to produce 6.53 g of ammonium sulfate.