A welder using a tank of volume 1¡Ñ10−2m3 fills it with oxygen (with a molar mass of 32.0g/mol ) at a gauge pressure of 1.4¡Ñ105Pa and temperature of 37.0∘C. Find the initial mass of oxygen. R=8.314m3PaK-1mol-1. The answer¡¦s unit is g.
To find the initial mass of oxygen in the tank, we need to use the ideal gas law equation:
PV = nRT
Where:
P = gauge pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, we need to convert the gauge pressure from pascal (Pa) to absolute pressure by adding the atmospheric pressure. Assuming the atmospheric pressure is 1 atm = 1.01325 x 10^5 Pa, we have:
Absolute Pressure (P') = Gauge Pressure (P) + Atmospheric Pressure = 1.4 x 10^5 Pa + 1.01325 x 10^5 Pa
Next, we convert the volume from m^3 to liters (L):
Volume (V') = Volume (V) x 1000 = 1 x 10^-2 m^3 x 1000 = 10 L
Next, we convert the temperature from Celsius (°C) to Kelvin (K):
Temperature (T') = Temperature (T) + 273.15 = 37.0°C + 273.15 = 310.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
Substituting the values we have:
n = P'V' / RT = (2.41325 x 10^5 Pa)(10 L) / (8.314 m^3 Pa K^-1 mol^-1)(310.15 K)
Calculating this expression gives us the number of moles:
n ≈ 0.947 mol
Finally, we can calculate the initial mass of oxygen using the molar mass of oxygen (32.0 g/mol):
Initial mass of oxygen = n x molar mass of oxygen = 0.947 mol x 32.0 g/mol
Calculating this expression gives us the initial mass of oxygen:
Initial mass of oxygen ≈ 30.30 g
Therefore, the initial mass of oxygen in the tank is approximately 30.30 grams.
To find the initial mass of oxygen, we can use the ideal gas law equation:
PV = nRT
Where:
P = gauge pressure = 1.4 × 105 Pa
V = volume = 1 × 10−2 m3
n = number of moles of oxygen
R = ideal gas constant = 8.314 m3PaK−1mol−1
T = temperature in Kelvin
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 37.0 + 273.15
T(K) = 310.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = PV / RT
n = (1.4 × 105 Pa) × (1 × 10−2 m3) / (8.314 m3PaK−1mol−1) × (310.15 K)
n = 0.053073 mol
Next, we can calculate the initial mass of oxygen using the molar mass:
Mass = n × molar mass
Mass = 0.053073 mol × 32.0 g/mol
Mass = 1.69752 g
Therefore, the initial mass of oxygen is approximately 1.70 g.