The temperature of a copper bar with a diameter of 50 mm and a length of 1 m is increased by 95°c. The increase in volume is 9 513 mm3. Calculate the density of oxygen is 1.42kg/m3 at standard temperature and pressure (STP).
Calculate the density of oxygen of 30°C and a pressure of 9×10 square 4 PA. The gas constant of oxygen is 261.311 j/kg. K
To calculate the density of oxygen at 30°C and a pressure of 9×10^4 Pa using the ideal gas law, we can use the following formula:
PV = nRT
Where:
P = Pressure (in Pa)
V = Volume (in m^3)
n = Number of moles
R = Gas constant (in J/kg·K)
T = Temperature (in K)
First, let's convert the given values to the appropriate units:
Temperature:
Given: 30°C
To convert from Celsius to Kelvin, we add 273.15:
T = 30°C + 273.15 = 303.15 K
Pressure:
Given: 9×10^4 Pa
Volume:
The volume of oxygen is not directly given in the question. We can use the ideal gas law equation to find the volume using the known values from standard temperature and pressure (STP) conditions.
Let's use the STP conditions:
STP temperature = 273.15 K
STP pressure = 1 atm = 101325 Pa
Using the ideal gas law, we have:
PV = nRT
Substituting the STP values:
(101325 Pa)(V) = (n)(261.311 J/kg·K)(273.15 K)
To find the number of moles (n), we need the molar mass of oxygen (O2).
The molar mass of oxygen is approximately 32 g/mol.
Using the molar mass calculation:
Molar mass of oxygen = 32 g/mol
Convert the given density from kg/m^3 to g/m^3 by multiplying by 1000:
Density of oxygen at STP = 1.42 kg/m^3 * 1000 = 1420 g/m^3
Now, we can calculate the number of moles:
n = (mass of substance) / (molar mass)
n = (density) * (volume) / (molar mass)
n = (1420 g/m^3) * (V) / (32 g/mol)
Substituting the equations for n into the ideal gas law equation, we have:
(101325 Pa)(V) = [(1420 g/m^3) * (V) / (32 g/mol)](261.311 J/kg·K)(273.15 K)
Solving for V, we find:
V = [(32 g/mol) * (101325 Pa) * (273.15 K)] / [(1420 g/m^3) * (261.311 J/kg·K)]
Now that we have the value of volume (V), we can calculate the density of oxygen at 30°C and a pressure of 9×10^4 Pa using the ideal gas law formula PV = nRT:
Density = (mass of substance) / (volume)
Density = [(density at STP) * (V)] / (mass of substance)
Density = [(1420 g/m^3) * (V)] / (32 g/mol)
Plug in the calculated value of V and the known values to find the density of oxygen at 30°C and a pressure of 9×10^4 Pa.