If 0.5000grams of barium carbonate was reacted with 25.0mLs of 0.15M nitric acid and the gas then collected in 100mL flask at 77°C, what is the gas pressure in the flask?
I assume the vapor pressure of H2O at 77 C is ignored as well as the volume occupied by the liquid HNO3.
This a limiting reagent problem coupled to a gas law PV = nRT problem.
BaCO3 + 2HNO3 ==> Ba(NO3)2 + CO2 + H2O
mols BaCO3 = grams/molar mass = ?
mols HNO3 = M x L = ?
Convert mols BaCO3 to mols CO2 using the coefficients in the balanced equation.
Do the same for mols HNO3 to mols CO2.
It is likely that the values for mols CO2 will not agree which means one of them is wrong. The correct value in limiting reagent problems is ALWAYS the smaller value and the reagent providing that number is the limiting reagent.
Then use PV = nRT and the smaller mols to obtain pressure.
To determine the gas pressure in the flask, we can use the ideal gas law, which states that the product of pressure (P), volume (V), and the number of moles of gas (n), is equal to the product of the gas constant (R) and the temperature (T) in Kelvin.
The formula for the ideal gas law is: PV = nRT
First, we need to calculate the number of moles of gas produced in the reaction involving barium carbonate and nitric acid.
1. Calculate the number of moles of barium carbonate (BaCO3):
Given mass of BaCO3 = 0.5000 grams
Molar mass of BaCO3 = 137.33 g/mol (barium: 137.33 g/mol, carbon: 12.01 g/mol, oxygen: 3 x 16.00 g/mol)
Number of moles of BaCO3 = mass / molar mass = 0.5000 g / 137.33 g/mol
2. Write and balance the chemical equation for the reaction:
BaCO3 + 2HNO3 -> Ba(NO3)2 + CO2 + H2O
From the balanced equation, we can see that 1 mole of BaCO3 produces 1 mole of CO2.
3. Since the molar ratio of BaCO3 to CO2 is 1:1, the number of moles of CO2 formed will be the same as the number of moles of BaCO3.
4. Now, let's calculate the number of moles of CO2 (n):
Number of moles of CO2 = Number of moles of BaCO3 = 0.5000 g / 137.33 g/mol
Next, we need to convert the given volume of the flask into liters and the temperature into Kelvin.
5. Convert the volume from milliliters (mL) to liters (L):
Given volume of the flask = 100 mL
Volume in liters = 100 mL / 1000 mL/L = 0.100 L
6. Convert the temperature from Celsius to Kelvin:
Given temperature = 77°C
Temperature in Kelvin = 77°C + 273.15 = 350.15 K
Now, we can substitute the values into the ideal gas law equation and solve for the gas pressure (P):
PV = nRT
P * 0.100 L = (0.5000 g / 137.33 g/mol) * (0.0821 L·atm/mol·K) * 350.15 K
Simplifying the equation gives:
P = (0.5000 g / 137.33 g/mol) * (0.0821 L·atm/mol·K) * 350.15 K / 0.100 L
Now, you can calculate the gas pressure using the given values:
P = (0.5000 * 0.0821 * 350.15) / (137.33 * 0.100)
The calculated pressure will be in atm (atmospheric pressure).