Alka-Seltzer contains the base sodium hydrogen carbonate, NaHCO3, which reacts with hydrochloric acid in the stomach to yield sodium chloride, carbon dioxide, and water. What volume of CO2 gas at 104.5 kPa and 311 K would be formed when 10.0 mL of 1.0 M HCl is mixed with an excess of NaHCO3?
To find the volume of CO2 gas formed, we need to use the balanced chemical equation for the reaction between NaHCO3 and HCl.
The balanced equation is as follows:
2 NaHCO3 + 2 HCl → 2 NaCl + 2 H2O + 2 CO2
From the balanced equation, we can see that 2 moles of NaHCO3 produce 2 moles of CO2. Therefore, to find the moles of CO2 produced, we can calculate the moles of NaHCO3 used.
Step 1: Convert the volume of HCl to moles
Given:
Volume of HCl: 10.0 mL
Molarity of HCl: 1.0 M
First, we need to convert the volume of HCl to moles using the formula:
moles = volume (L) x concentration (mol/L)
Converting 10.0 mL to liters:
Volume (L) = 10.0 mL / 1000 = 0.01 L
Now, we can calculate the moles of HCl:
moles of HCl = volume (L) x concentration (mol/L) = 0.01 L x 1.0 mol/L = 0.01 mol
Step 2: Calculate the moles of CO2 produced
Since the reaction is 2:2 ratio between NaHCO3 and CO2, the moles of CO2 produced would be equal to the moles of NaHCO3 used.
moles of CO2 = moles of NaHCO3 = 0.01 mol
Step 3: Convert moles of CO2 to volume
We can use the ideal gas law:
PV = nRT
Where:
P = Pressure (104.5 kPa)
V = Volume (unknown)
n = moles of CO2 (0.01 mol)
R = Ideal gas constant (8.31 J/(mol·K))
T = Temperature (311 K)
Rearranging the equation to solve for V:
V = (nRT) / P
Substituting the values:
V = (0.01 mol x 8.31 J/(mol·K) x 311 K) / 104.5 kPa
Converting kPa to Pa:
V = (0.01 mol x 8.31 J/(mol·K) x 311 K) / (104.5 x 1000 Pa)
Simplifying:
V = (2559.81 J) / (104500 Pa)
V = 0.0245 L or 24.5 mL
Therefore, the volume of CO2 gas formed when 10.0 mL of 1.0 M HCl is mixed with an excess of NaHCO3 is 24.5 mL.
To find the volume of CO2 gas that would be formed when HCl reacts with NaHCO3, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature
First, we need to determine the number of moles of CO2 gas produced. According to the balanced chemical equation, the reaction between HCl and NaHCO3 produces 1 mole of CO2.
Given that we have an excess of NaHCO3, we can assume that all of the HCl reacts, and therefore, 1 mole of CO2 is produced.
Now, let's calculate the volume of CO2 gas using the ideal gas law equation. We have:
P = 104.5 kPa (convert to atm by dividing by 101.325 kPa/atm)
V = ?
n = 1 mole
R = 0.0821 atm·L/(mol·K) (ideal gas constant in suitable units)
T = 311 K
Rearranging the equation, we have:
V = (nRT) / P
Substituting the values, we get:
V = (1 mole * 0.0821 atm·L/(mol·K) * 311 K) / 104.5 kPa (convert to atm)
Now, let's do the calculations:
V = (1 * 0.0821 * 311) / 0.1045
V = 24.51 L
Therefore, the volume of CO2 gas formed when 10.0 mL of 1.0 M HCl reacts with an excess of NaHCO3 is 24.51 L at 104.5 kPa and 311 K.
NaHCO3 + HCl ==> NaCl + H2O + CO2
mols HCl = M x L = ?
Use the coefficients in the balanced equation to convert mols HCl to mols CO2.
Then use PV = nRT to convert mols CO2 to L at the conditions listed.