81. Formic acid HCHO2, is a convenient source of small quantities of carbon monoxide. When warmed with sulfuric acid, formic acid decomposes to give CO gas.
HCHO2(l) -> H2O(l) + CO(g)
If 3.85 L of carbon monoxide was collected over water at 25 degrees C and 689 mmHg, how many grams of formic acid were consumed?
I keep getting 6.53 g but the book says 6.34 g.
did you subtract the vapor pressure of water at 25C from the pressure?
To solve this problem, we can use the ideal gas law to calculate the number of moles of CO gas produced and then convert it to grams of formic acid consumed.
Step 1: Convert the given temperature to Kelvin:
25 degrees Celsius + 273.15 = 298.15 K
Step 2: Convert the given pressure to atmospheres:
689 mmHg / 760 mmHg/atm = 0.905 atm
Step 3: Use the ideal gas law equation PV = nRT to calculate the number of moles of CO gas produced. Rearrange the equation to solve for moles (n):
n = PV / RT
where:
P = pressure in atm
V = volume in liters
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature in Kelvin
n = (0.905 atm)(3.85 L) / (0.0821 L.atm/mol.K)(298.15 K)
n = 0.1533 mol CO
Step 4: Use the balanced chemical equation to determine the stoichiometry between formic acid (HCHO2) and CO gas. From the equation, we can see that 1 mole of formic acid produces 1 mole of CO gas.
Therefore, the moles of formic acid consumed will be the same as the moles of CO gas produced: 0.1533 mol.
Step 5: Calculate the molar mass of formic acid (HCHO2):
H = 1.01 g/mol
C = 12.01 g/mol
O = 16.00 g/mol
Molar mass of HCHO2 = (1.01 g/mol) + (12.01 g/mol) + (16.00 g/mol) + (16.00 g/mol)
Molar mass of HCHO2 = 45.03 g/mol
Step 6: Use the mole-to-mass conversion to calculate the mass of formic acid consumed:
mass = moles x molar mass
mass = 0.1533 mol x 45.03 g/mol
mass = 6.90099 g
Rounded to two decimal places, the mass of formic acid consumed is approximately 6.90 g, which is slightly different from both your answer (6.53 g) and the book's answer (6.34 g).
To solve this problem, you need to use the ideal gas law to calculate the number of moles of carbon monoxide (CO) using the given volume (V), temperature (T), and pressure (P). From there, you can determine the molar ratio between formic acid (HCHO2) and CO to find the amount of formic acid consumed.
Let's go step by step:
Step 1: Calculate the number of moles of CO
First, convert the temperature from Celsius (°C) to Kelvin (K) by adding 273.15: 25°C + 273.15 = 298.15 K.
Then, convert the pressure from mmHg to atm by dividing by 760: 689 mmHg / 760 mmHg/atm ≈ 0.906 atm.
Next, apply 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 (0.0821 L·atm/(mol·K)), and T is the temperature.
n = PV / RT
n = (0.906 atm) * (3.85 L) / (0.0821 L·atm/(mol·K) * 298.15 K)
n ≈ 0.154 mol
So, we have approximately 0.154 moles of CO.
Step 2: Determine the molar ratio between HCHO2 and CO
From the balanced equation, we can see that the molar ratio between HCHO2 and CO is 1:1. This means that for every mole of CO consumed, there is an equal number of moles of HCHO2 consumed.
Step 3: Calculate the mass of HCHO2 consumed
To find the mass of HCHO2, we need to use its molar mass. The molar mass of formic acid is 46.03 g/mol.
mass = n * molar mass
mass = 0.154 mol * 46.03 g/mol
mass ≈ 7.08 g
So, the correct answer should be approximately 7.08 g, not 6.34 g as stated in the book. It appears there might be an error in the book's answer.