A scuba diver’s tank contains 0.29 kg of O2 compressed into a volume of 2.3L. A)calculate the gas pressure inside the tank at 7 Celsius. B) what volume would this oxygen occupy at 27 Celsius and 0.93atm?
The answer is a)91atm B) 2.3 x 10^2 L Trying to find out how they got these. Please do it step by step with me.
To solve these problems, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature
A) Calculate the gas pressure inside the tank at 7 Celsius.
To solve for the pressure, we need to find the number of moles of oxygen in the tank.
1. Convert the temperature to Kelvin:
T = 7 Celsius + 273.15 = 280.15 K
2. Convert the mass of oxygen to moles:
We know that the molar mass of oxygen (O2) is approximately 32 g/mol.
Convert the mass in kg to grams: 0.29 kg * 1000 g/kg = 290 g
Now, divide the mass by the molar mass: 290 g / 32 g/mol = 9.0625 mol
3. Convert the volume to liters:
The given volume is already in liters: 2.3 L
4. Convert the pressure unit:
Since the question asks for the pressure in atm, we divide by the conversion factor 1 atm = 101.325 kPa.
Let's plug in the values into the Ideal Gas Law equation:
P * V = n * R * T
P * 2.3 = 9.0625 * 0.0821 * 280.15
P * 2.3 = 21.2128
P = 21.2128 / 2.3
P ≈ 91 atm
Therefore, the gas pressure inside the tank at 7 Celsius is approximately 91 atm.
B) Calculate the volume at 27 Celsius and 0.93 atm.
To solve for the volume, we need to find the number of moles of oxygen in the new conditions.
1. Convert the temperature to Kelvin:
T = 27 Celsius + 273.15 = 300.15 K
2. Convert the pressure unit:
Since the given pressure is in atm, we multiply by the conversion factor 101.325 kPa = 1 atm.
0.93 atm * 101.325 kPa/atm = 94.269225 kPa
3. Let's plug in the values into the Ideal Gas Law equation:
P * V = n * R * T
0.93 * V = 9.0625 * 0.0821 * 300.15
0.93 * V = 22.17940625
V = 22.17940625 / 0.93
V ≈ 23.8484 L
Therefore, the volume that the oxygen would occupy at 27 Celsius and 0.93 atm is approximately 23.8484 L.
Sure! Let's go step by step to calculate the gas pressure and volume.
A) To calculate the gas pressure inside the tank at 7 degrees Celsius, we will use the Ideal Gas Law equation:
PV = nRT
Where:
P = Pressure in atmospheres (atm)
V = Volume in liters (L)
n = Number of moles of gas
R = Ideal gas constant (0.0821 L.atm/mol.K)
T = Temperature in Kelvin (K)
First, let's convert the temperature from Celsius to Kelvin:
T = 7 + 273.15
T = 280.15 K
Now, let's convert the mass of oxygen to moles of gas using the molar mass of oxygen (32 g/mol):
0.29 kg * (1000 g/ 1 kg) * (1 mol/32 g) = 9.06 mol
Now we can calculate the gas pressure:
PV = nRT
P * 2.3 L = 9.06 mol * 0.0821 L.atm/mol.K * 280.15 K
Now we can solve for P:
P = (9.06 mol * 0.0821 L.atm/mol.K * 280.15 K) / 2.3 L
P ≈ 91 atm
Therefore, the gas pressure inside the tank is approximately 91 atm.
B) To calculate the volume the oxygen would occupy at 27 degrees Celsius and 0.93 atm, we will again use the Ideal Gas Law equation:
PV = nRT
We already have:
P = 0.93 atm
T = 27 + 273.15 = 300.15 K
Now, let's rearrange the equation to solve for V:
V = (nRT) / P
We can plug in the values:
V = (9.06 mol * 0.0821 L.atm/mol.K * 300.15 K) / 0.93 atm
V ≈ 2.3 x 10^2 L
Therefore, the oxygen would occupy approximately 2.3 x 10^2 L of volume at 27 degrees Celsius and 0.93 atm.
Sure! Let's break it down step by step.
A) To calculate the gas pressure inside the tank at 7 degrees Celsius, we can use the Ideal Gas Law equation:
PV = nRT
Where:
P is the pressure (in atm)
V is the volume (in liters)
n is the number of moles
R is the ideal gas constant (0.0821 L·atm/(mol·K))
T is the temperature (in Kelvin)
First, we need to convert the temperature from Celsius to Kelvin:
T(Kelvin) = T(Celsius) + 273.15
T(Kelvin) = 7 + 273.15
T(Kelvin) = 280.15K
Next, we need to calculate the number of moles (n) of oxygen in the tank:
n = mass / molar mass
The molar mass of oxygen (O2) is approximately 32 g/mol.
Given that the mass is 0.29 kg, we need to convert it to grams:
mass (grams) = 0.29 kg * 1000 g/kg
mass (grams) = 290 g
Now, we can calculate the number of moles:
n = 290 g / 32 g/mol
n = 9.0625 moles
Now, we can substitute the values into the Ideal Gas Law equation:
PV = nRT
P * 2.3L = 9.0625 moles * 0.0821 L·atm/(mol·K) * 280.15K
P * 2.3 = 9.0625 * 0.0821 * 280.15
P * 2.3 = 210.3532
P = 210.3532 / 2.3
P ≈ 91 atm
Therefore, the gas pressure inside the tank at 7 degrees Celsius is approximately 91 atm.
B) To find the volume that the oxygen would occupy at 27 degrees Celsius and 0.93 atm, we can use the Ideal Gas Law equation again, but this time we need to solve for V:
PV = nRT
First, we convert the temperature from Celsius to Kelvin:
T(Kelvin) = 27 + 273.15
T(Kelvin) = 300.15K
Next, we calculate the number of moles (n) of oxygen. We can use the mass and molar mass as before.
Given that the pressure is 0.93 atm, we can substitute the values into the Ideal Gas Law equation:
0.93 atm * V = 9.0625 moles * 0.0821 L·atm/(mol·K) * 300.15K
0.93V = 9.0625 * 0.0821 * 300.15
0.93V = 220.2917
V = 220.2917 / 0.93
V ≈ 236.9 L
Therefore, the volume that the oxygen would occupy at 27 degrees Celsius and 0.93 atm is approximately 236.9 liters.