A 20-cm-diameter cylinder that is 40 cm long contains 50 g of oxygen gas at 20C.
What is the number density of the oxygen? in m^-3
What is the reading of a pressure gauge attached to the tank? in kPa
Well, I'm not exactly an oxygen expert, but I'll give it a shot.
To find the number density of the oxygen gas, we need to find the number of oxygen molecules in the cylinder.
The volume of the cylinder can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Since the diameter of the cylinder is given as 20 cm, the radius is half of that, which is 10 cm or 0.1 m. The height of the cylinder is given as 40 cm or 0.4 m.
So, using the formula, the volume of the cylinder is V = π(0.1)^2(0.4) = 0.01257 m^3.
Now, to find the number of oxygen molecules, we need to use Avogadro's number, which is roughly 6.022 x 10^23.
Since we know the mass of the oxygen gas is 50 g, we can use the molar mass of oxygen, which is roughly 32 g/mol, to find the number of moles:
Number of moles = mass/molar mass = 50 g/32 g/mol = 1.5625 mol.
Finally, the number density of oxygen can be calculated by dividing the number of moles by the volume of the cylinder:
Number density = number of moles/volume = 1.5625 mol/0.01257 m^3 = 124.14 mol/m^3.
So, the number density of the oxygen gas is approximately 124.14 mol/m^3.
As for the reading of the pressure gauge attached to the tank, I'm not really sure. But if you tell me how tight the screws on the gauge are, I can give you a torque answer instead!
To find the number density of the oxygen, we first need to calculate the volume of the cylinder.
1. Calculate the radius of the cylinder:
The diameter is given as 20 cm, so the radius is half of that.
radius = diameter / 2 = 20 cm / 2 = 10 cm
2. Convert the radius to meters:
The radius is currently in centimeters, so we need to convert it to meters.
radius = 10 cm = 10 cm / 100 cm/m = 0.1 m
3. Calculate the volume of the cylinder:
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
volume = π * (radius)^2 * height
= π * (0.1 m)^2 * 0.4 m
= 0.04π m^3
4. Calculate the number density:
The number density is given by the formula n = N/V, where N is the number of particles and V is the volume.
number density = N / V
= mass / (Molar mass * V)
= mass / (Molar mass * volume)
= 0.05 kg / (0.032 kg/mol * 0.04π m^3)
= 0.05 / (0.032 * 0.04π) mol/m^3
The number density of oxygen gas is approximately 19.7 mol/m^3.
To find the reading of a pressure gauge attached to the tank, we need to use 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 gas constant, and T is the temperature in Kelvin.
5. Convert the temperature from Celsius to Kelvin:
Add 273 to the temperature to convert from Celsius to Kelvin.
Temperature (T) = 20°C + 273 = 293K
6. Rearrange the equation to solve for pressure (P):
P = nRT/V
7. Calculate the pressure:
Using the calculated number of moles (n = 0.05kg / 0.032 kg/mol) and the ideal gas constant (R = 8.3145 J/(mol·K)), we can substitute the values into the equation:
P = (0.05kg / 0.032 kg/mol) * (8.3145 J/(mol·K)) * 293K / (0.04π m^3)
The pressure gauge reading is approximately the calculated value in pascals (Pa). To convert it to kilopascals (kPa), divide the value by 1000.
Please note that this calculation assumes ideal gas behavior and that the gas is in equilibrium.
To calculate the number density of oxygen gas in the given cylinder, we need to determine the number of oxygen molecules present and the volume of the cylinder.
First, let's calculate the volume of the cylinder:
The cylinder has a diameter of 20 cm, which means its radius is 10 cm or 0.1 m (since 1 cm equals 0.01 m). The height or length of the cylinder is given as 40 cm or 0.4 m.
The volume of a cylinder can be calculated using the formula:
Volume = π * r^2 * h
Substituting the values:
Volume = π * (0.1 m)^2 * 0.4 m
Volume = 0.04π m^3
Next, we need to calculate the number of oxygen molecules present in the cylinder. To do this, we'll use the ideal gas equation:
PV = nRT
Where:
P is the pressure,
V is the volume,
n is the number of moles,
R is the ideal gas constant (8.314 J/(mol·K)), and
T is the temperature in Kelvin.
Since we're looking for the number density (the number of molecules per unit volume), we need to isolate n on one side of the equation:
n = PV / (RT)
To find the number of moles, we need to convert the given mass of oxygen gas into moles. To do this, we'll use the molar mass of oxygen, which is approximately 32 g/mol.
Number of moles = mass of oxygen / molar mass of oxygen
Number of moles = 50 g / 32 g/mol
Number of moles ≈ 1.5625 mol
Now we can calculate the number density:
Number density = Number of moles / Volume
Number density = 1.5625 mol / 0.04π m^3
To answer the second part of your question, we need more information. The ideal gas equation can help us find the reading on the pressure gauge, but we need to know the value of pressure (P) or the temperature (T) in Kelvin.
Please provide the value of either the pressure or the temperature so we can calculate the reading of the pressure gauge in kilopascals (kPa).
p•V =m•R•T/μ,
T= 293
μ =32000
p = m•R•T/V•μ
Density = m/V = p•μ/R•T