How much amount of CaCO3 in gm having % purity 50 percent produces 0.56 litre of CO2 at STP on heating. (Answer 5)
CaCO3 ==> CaO + CO2
Use PV = nRT and solve for n for CO2
Convert mols CO2 to mols CaCO3, then to grams CaCO3
Finally, multiply g CaCO3 by 2 since it is only 50% pure.
To find the amount of CaCO3 in grams, we need to use the information given. Let's break down the problem step-by-step:
1. We know that the purity of CaCO3 is 50%. This means that only half of the given sample is actually CaCO3, and the remaining half is impurities.
2. We also know that the CaCO3 sample produces 0.56 liters of CO2 at STP (Standard Temperature and Pressure). STP conditions represent a temperature of 0 degrees Celsius and a pressure of 1 atmosphere.
To solve the problem, we can follow these steps:
Step 1: Calculate the number of moles of CO2 produced.
To do this, we need to use the ideal gas law, which states that PV = nRT. At STP, the pressure (P) is 1 atm, the volume (V) is 0.56 L, and the temperature (T) is 0 degrees Celsius (273.15 Kelvin). The ideal gas constant (R) is 0.0821 L·atm/mol·K.
Using the ideal gas law, we can rearrange the equation to solve for the number of moles (n) of CO2:
n = PV / RT
Substituting the known values:
n = (1 atm) * (0.56 L) / (0.0821 L·atm/mol·K * 273.15 K)
Calculating the value of n gives us the number of moles of CO2 produced.
Step 2: Determine the number of moles of CaCO3 that reacted.
CaCO3 reacts according to the following balanced chemical equation:
CaCO3(s) → CaO(s) + CO2(g)
From the balanced equation, we can see that 1 mole of CaCO3 produces 1 mole of CO2. Therefore, the number of moles of CaCO3 is equal to the number of moles of CO2 produced.
Step 3: Calculate the mass of CaCO3.
To find the mass of CaCO3, we multiply the number of moles of CaCO3 calculated in step 2 by its molar mass. The molar mass of CaCO3 is the sum of the atomic masses of calcium (Ca), carbon (C), and three oxygen (O) atoms.
Add up the atomic masses from the periodic table to find the molar mass of CaCO3.
Step 4: Adjust for the purity.
Since the given percentage purity is 50%, we need to consider that only half of the mass calculated in step 3 is pure CaCO3. Multiply the calculated mass by 0.5 to find the actual mass of CaCO3.
You should now have the answer, which is the mass of CaCO3 in grams.