2HCl (aq) + K2CO3(aq) → H2O ( l ) + 2 KCl (aq)+ CO2 (g) A total of 2.0 moles of potassium carbonate and 3.0 moles of hydrochloric acid are combined; the reaction proceeds to completion.
a. Which reactant is limiting?
b. How many moles of carbon dioxide are formed?
c. What is the mass of carbon dioxide that is formed?
d. How many moles of water are formed?
e. What is the mass of water that is formed?
f. Water has a density of 1.00 g/mL at room temperature. What volume of water is produced?
g. Carbon dioxide is a gas. It turns out that 1.00 moles of any gas occupies 24.0 L at 20 ̊C under 1.00 atmospheres (atm) of pressure. What volume of carbon dioxide (at 20 ̊C under 1.00 atm) is formed?
To determine the limiting reactant, we need to calculate the moles of products formed from each reactant and compare them. The reactant that produces the least amount of product is the limiting reactant.
a. First, let's calculate the moles of carbon dioxide (CO2) formed from each reactant.
From the balanced equation, we see that the coefficient of K2CO3 is 1, and the coefficient of CO2 is also 1, meaning they have a 1:1 mole ratio.
Moles of CO2 from K2CO3 = 2.0 moles of K2CO3
From the balanced equation, we see that the coefficient of HCl is 2, and the coefficient of CO2 is 1, meaning they have a 2:1 mole ratio.
Moles of CO2 from HCl = (2.0 moles of HCl) * (1 mole CO2 / 2 moles HCl) = 1.0 moles of CO2
Therefore, the limiting reactant is HCl because it produces fewer moles of CO2.
b. The number of moles of carbon dioxide formed is 1.0 moles.
c. To calculate the mass of carbon dioxide formed, we need to use the molar mass of CO2. The molar mass of CO2 is 44.01 g/mol.
Mass of CO2 = (1.0 moles) * (44.01 g/mol) = 44.01 g
Therefore, the mass of carbon dioxide formed is 44.01 g.
d. From the balanced equation, we see that the coefficient of H2O is 1, meaning they have a 1:1 mole ratio with HCl.
Moles of H2O = 3.0 moles of HCl
Therefore, the number of moles of water formed is 3.0 moles.
e. The molar mass of water (H2O) is 18.02 g/mol.
Mass of H2O = (3.0 moles) * (18.02 g/mol) = 54.06 g
Therefore, the mass of water formed is 54.06 g.
f. Water has a density of 1.00 g/mL. The mass of the water formed is 54.06 g, so the volume can be calculated using the density formula:
Volume of water = (Mass of water) / (Density of water)
Volume of water = (54.06 g) / (1.00 g/mL) = 54.06 mL
Therefore, the volume of water produced is 54.06 mL.
g. To calculate the volume of carbon dioxide (CO2) formed, we need to use the ideal gas law equation:
PV = nRT
P = 1.00 atm, V = ?, n = 1.0 moles, R = 0.0821 L·atm/(mol·K), T = 20 ̊C = 293 K (convert to Kelvin)
Rearranging the equation, we have:
V = (nRT) / P
V = (1.0 moles) * (0.0821 L·atm/(mol·K)) * (293 K) / (1.00 atm)
V = 23.91 L
Therefore, the volume of carbon dioxide formed is 23.91 L.