A 8.60-g sample of solid CaSO4·2H2O was heated such that the water turned to steam and was driven off. Assuming ideal behavior, what volume would that steam occupy at 1.00 atm and 100.0 °C?
Why did the steam go to therapy?
Because it had a lot of pressure and needed someone to vent to!
Now, let's get down to business. To solve this problem, we'll need to use the ideal gas law. The ideal gas law states that PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to find the number of moles of water. The molar mass of H2O is 18 g/mol, so the number of moles is:
moles = mass / molar mass
moles = 8.60 g / 18 g/mol
moles ≈ 0.478 mol
Now, let's convert the temperature to Kelvin:
T = 100.0 °C + 273.15
T ≈ 373.15 K
Next, let's plug our values into the ideal gas law equation:
PV = nRT
V = nRT / P
V = (0.478 mol)(0.0821 L·atm/mol·K)(373.15 K) / 1.00 atm
V ≈ 14.3 L
So, the volume of steam at 1.00 atm and 100.0 °C would be approximately 14.3 liters. It's always good to remember that the ideal gas law is just a "theory," but for practical purposes, it usually gets the job done!
To determine the volume of steam produced, we need to use the ideal gas law equation, which is PV = nRT, where:
- P is the pressure (1.00 atm),
- V is the volume,
- n is the number of moles of the gas,
- R is the ideal gas constant (0.0821 L·atm/mol·K),
- T is the temperature in Kelvin.
First, we need to calculate the number of moles of steam produced:
1. Calculate the molar mass of water (H2O):
- Hydrogen (H) has a molar mass of 1 g/mol, and there are 2 hydrogen atoms in water.
- Oxygen (O) has a molar mass of 16 g/mol.
- Therefore, the molar mass of water (H2O) = (2 * 1 g/mol) + (1 * 16 g/mol) = 18 g/mol.
2. Convert the mass of water (given in grams) to moles:
- Mass of water = 8.60 g
- Moles of water = Mass of water / Molar mass of water
= 8.60 g / 18 g/mol
≈ 0.478 moles.
Since we have 2 moles of water (H2O) per mole of steam (H2O), the number of moles of steam produced is also 0.478 moles.
Next, we need to convert the temperature from Celsius to Kelvin:
1. Convert 100.0 °C to Kelvin:
- Kelvin (K) = Celsius (°C) + 273.15
- Kelvin = 100.0 °C + 273.15
= 373.15 K.
Now, we can calculate the volume of steam produced using the ideal gas law equation:
PV = nRT
V = (nRT) / P
= (0.478 mol * 0.0821 L·atm/mol·K * 373.15 K) / 1.00 atm
≈ 14.7 L.
Therefore, the volume of steam produced at 1.00 atm and 100.0 °C would be approximately 14.7 liters.
To determine the volume that the steam would occupy at 1.00 atm and 100.0 °C, we can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure (in atm)
V = Volume (in liters)
n = Number of moles
R = Ideal gas constant (0.0821 L·atm/mol·K)
T = Temperature (in Kelvin)
We need to start by calculating the number of moles of water vapor (steam) produced when the solid CaSO4·2H2O is heated.
Step 1: Calculate the number of moles of water in the sample.
The molar mass of CaSO4·2H2O can be calculated using the atomic masses from the periodic table.
Ca: 40.08 g/mol
S: 32.06 g/mol
O: 16.00 g/mol
H: 1.01 g/mol
Molar mass of H2O = 2(1.01 g/mol) + 16.00 g/mol = 18.02 g/mol
Number of moles of water = mass of water / molar mass of water
= 8.60 g / 18.02 g/mol
Step 2: Calculate the volume using the ideal gas law.
Convert the temperature from degrees Celsius to Kelvin: T(K) = T(°C) + 273.15
T(K) = 100.0 °C + 273.15 = 373.15 K
Now we can use the ideal gas law equation to solve for the volume (V):
PV = nRT
P = 1.00 atm
T = 373.15 K
R = 0.0821 L·atm/mol·K
n = moles of water (from Step 1)
V = (nRT) / P
V = (moles of water) * (R) * (T) / P
Substitute the calculated values into the equation to calculate the volume (V).
Calculate %H2O in CaSO4.2H2O by
(2*molar mass H2O/molar mass CaSO4.2H2O)*100 = ?
8.60g sample x %H20/100 = grams H2O driven off. Convert to mols. Then use PV = nRT and the conditions listed and solve for V in Liters.