Consider the following chemical reaction:
2 KNO3 (s) ------------> 2 KNO2 (s) + O2 (g)
What volume, in liters, of O2 at 31.2oC and 2.045 atm pressure can be produced from the decomposition of 54.92 g of KNO3 (FM = 101.1 g/mol).
To solve this problem, we will use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
First, we need to calculate the number of moles of KNO3. We can use the molar mass of KNO3 to convert grams to moles.
molar mass of KNO3 = 101.1 g/mol
moles of KNO3 = mass / molar mass
moles of KNO3 = 54.92 g / 101.1 g/mol = 0.5434 mol
According to the balanced chemical equation, 2 moles of KNO3 will produce 1 mole of O2. Therefore, the number of moles of O2 produced is half the number of moles of KNO3:
moles of O2 = 0.5434 mol / 2 = 0.2717 mol
Now, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 31.2 + 273.15 = 304.35 K
Now, we can substitute the values into the ideal gas law equation and solve for volume:
PV = nRT
V = (nRT) / P
V = (0.2717 mol * 0.0821 L·atm/mol·K * 304.35 K) / 2.045 atm
V ≈ 4.06 L
Therefore, the volume of O2 produced from the decomposition of 54.92 g of KNO3 is approximately 4.06 liters at 31.2°C and a pressure of 2.045 atm.
To solve this problem, we need to 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 ideal gas constant, and T is the temperature in Kelvin.
First, let's calculate the number of moles of KNO3 using its molar mass:
Molar mass of KNO3 = 101.1 g/mol
Number of moles of KNO3 = mass of KNO3 / molar mass of KNO3
Number of moles of KNO3 = 54.92 g / 101.1 g/mol
Next, let's use the balanced chemical equation to determine the moles of O2 produced. According to the balanced equation, for every 2 moles of KNO3 decomposed, 1 mole of O2 is produced.
Number of moles of O2 = (Number of moles of KNO3) / 2
Now, let's convert the temperature to Kelvin:
Temperature in Kelvin = 31.2°C + 273.15
After obtaining the temperature in Kelvin, we can substitute the values into the ideal gas law equation and solve for the volume of O2:
(2.045 atm) * V = (Number of moles of O2) * (0.0821 L·atm/mol·K) * (Temperature in Kelvin)
Now, we have all the information needed to calculate the volume of O2. Let's plug in the values and solve for V:
V = [(Number of moles of O2) * (0.0821 L·atm/mol·K) * (Temperature in Kelvin)] / 2.045 atm
Substitute the values and calculate V to find the volume of O2.
Always start with a balanced equation. You have that.
Convert 54.92 g KNO3 to mols. mol = grams/molar mass = ?
Using the coefficients in the balanced equation, convert mols KNO3 (what you have) to mols of what you want (mols O2). Then convert that to volume using PV = nRT. That gives you V at the conditions listed. Remember T is in kelvin.