You have a reaction using the following criteria: 1.3456 g of barium chloride solution (0.786M) is mixed with 1.20089 g of sodium sulfate solution (1.3M). The ambient pressure is 754.564 mmHg and the temperature is 56.889 degrees celsius. Determine the volume of the gas produced.
To determine the volume of gas produced, we need to first identify the balanced chemical equation for the reaction between barium chloride (BaCl2) and sodium sulfate (Na2SO4). Once we have the balanced equation, we can use the stoichiometry of the reaction to find the number of moles of gas produced. Finally, using the ideal gas law, we can calculate the volume of gas produced.
Step 1: Write the balanced chemical equation:
BaCl2 + Na2SO4 -> BaSO4 + 2NaCl
Step 2: Calculate the moles of reactants:
moles of BaCl2 = mass of BaCl2 / molar mass of BaCl2
moles of Na2SO4 = mass of Na2SO4 / molar mass of Na2SO4
Given:
mass of BaCl2 = 1.3456 g
molar mass of BaCl2 = 137.327 g/mol
mass of Na2SO4 = 1.20089 g
molar mass of Na2SO4 = 142.042 g/mol
moles of BaCl2 = 1.3456 g / 137.327 g/mol
moles of Na2SO4 = 1.20089 g / 142.042 g/mol
Step 3: Determine the limiting reactant:
To identify the limiting reactant, we compare the moles of each reactant and use the stoichiometry of the balanced equation. The reactant that produces the fewer moles of product will be the limiting reactant.
Based on the balanced equation, 1 mole of BaCl2 reacts with 1 mole of Na2SO4 to produce 1 mole of BaSO4.
moles of BaSO4 (the product) = moles of limiting reactant
Step 4: Calculate the moles of gas produced:
From the balanced equation, we can see that for 1 mole of BaSO4 produced, 1 mole of gas is also produced.
moles of gas produced = moles of BaSO4
Step 5: Calculate the volume of the gas produced using the ideal gas law:
The ideal gas law equation is:
PV = nRT
Where:
P = pressure (in atm)
V = volume of gas (in liters)
n = moles of gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)
Given:
Pressure (P) = 754.564 mmHg
Temperature (T) = 56.889 degrees Celsius
However, for the ideal gas law, temperature must be in Kelvin. So, we convert the temperature using the equation:
T(K) = T(Celsius) + 273.15
Temperature (T) = 56.889 + 273.15
= 330.039 Kelvin
Now, we can plug in the values into the ideal gas law equation and rearrange to solve for V:
V = (n * R * T) / P
Substituting the values:
V = (moles of gas produced * 0.0821 L.atm/mol.K * 330.039 K) / 754.564 mmHg
Finally, convert mmHg to atm by dividing by 760 mmHg/atm:
V = (moles of gas produced * 0.0821 L.atm/mol.K * 330.039 K) / (754.564 mmHg / 760 mmHg/atm)
Calculating this expression will give you the volume of gas produced.