A cook puts 7.20 g of water in a 2.00-L pressure cooker that is then warmed to 530°C. What is the pressure inside the container? (Assume room temperature is 20°C.)
(2.00 L) x (273 / (20 + 273)) / (22.414 L/mol) = 0.083139 mol air in the "empty" container
(7.20 g H2O) / (18.01532 g H2O/mol) = 0.39966 mol H2O added
Supposing all the water vaporized:
PV = nRT
P = nRT / V = (0.083139 mol + 0.39966 mol) x (0.08205746 L atm/K mol) x
(530 + 273 K) / (2.00 L) = 15.9 atm
15.9atm x 101.3kPa = 1611.31
To solve this problem, we can use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure (unknown)
V = volume of the pressure cooker = 2.00 L
n = number of moles of water
R = ideal gas constant
T = temperature in Kelvin
To find the number of moles of water, we need to know its molecular weight (MW). The molecular weight of water (H2O) is approximately 18.015 g/mol.
To find the number of moles (n):
n = mass / molecular weight
n = 7.20 g / 18.015 g/mol
n ≈ 0.3996 mol
Now, let's convert the temperature from Celsius to Kelvin:
T = 530°C + 273.15
T ≈ 803.15 K
Now, we can substitute these values into the ideal gas law equation:
PV = nRT
P * 2.00 L = (0.3996 mol) * (0.0821 L·atm/mol·K) * 803.15 K
P * 2.00 L = 26.77 L·atm
P = 26.77 L·atm / 2.00 L
P ≈ 13.39 atm
Therefore, the pressure inside the container is approximately 13.39 atm.
To determine the pressure inside the container, we can use the ideal gas law equation, which is given by:
PV = nRT
Where:
P is the pressure (in units of Pa or atm)
V is the volume (in units of liters or m^3)
n is the number of moles of the gas
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature (in units of Kelvin)
To solve the problem, we need to convert the given information into appropriate units and calculate the number of moles:
1. The mass of water is given as 7.20 g. To find the number of moles, we use the molar mass of water, which is 18.015 g/mol. Therefore,
moles of water = (7.20 g) / (18.015 g/mol) = 0.3999 mol (approximately 0.40 mol)
2. The temperature is given in Celsius, so we need to convert it to Kelvin.
Temperature in Kelvin = (530°C + 273.15) = 803.15 K
Now we can substitute the values into the ideal gas law equation and solve for pressure:
PV = nRT
P * (2.00 L) = (0.40 mol) * (8.314 J/(mol·K)) * (803.15 K)
P = [(0.40 mol) * (8.314 J/(mol·K)) * (803.15 K)] / (2.00 L)
Simplifying the equation gives us:
P ≈ 134.8 atm
Therefore, the pressure inside the container is approximately 134.8 atm.