1.A scuba diver's tank contains 0.29 kg of O2 compressed into a volume of 2.3 L.
a)Calculate the gas pressure inside the tank when the temperature is 9oC.
b)calculate the volume of oxygen if the temperature is 26oC and the pressure is 0.095 atm.
somebody..plz help me...tq
Certainly! Let's break down each question step by step:
a) To calculate the gas pressure inside the tank when the temperature is 9°C, we can use the ideal gas law. The ideal gas law equation is given by: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
In order to apply the ideal gas law, we need to convert temperature from Celsius to Kelvin. The conversion formula is T(K) = T(°C) + 273.15.
Given:
- Volume (V) = 2.3 L
- Temperature (T) = 9°C
Converting the temperature to Kelvin:
T(K) = 9 + 273.15 = 282.15 K
We also need to consider the number of moles of gas (n) in order to use the ideal gas law. To find the number of moles (n), we can use the molar mass of oxygen (O₂), which is 32 g/mol.
Given:
- Mass (m) = 0.29 kg
- Molar mass (M) of O₂ = 32 g/mol
Converting mass to grams:
m(g) = 0.29 kg × 1000 g/kg = 290 g
Now, we can calculate the number of moles:
n(mol) = m(g) / M(g/mol) = 290 g / 32 g/mol = 9.0625 mol (approximately)
Now, we can use the ideal gas law equation to calculate the pressure (P). The ideal gas constant (R) is 0.0821 L·atm/(mol·K).
Rearranging the equation to solve for P:
P = (nRT) / V
Substituting the values:
P = (9.0625 mol × 0.0821 L·atm/(mol·K) × 282.15 K) / 2.3 L
Calculating the pressure (P):
P ≈ 11.07 atm
Therefore, the gas pressure inside the tank when the temperature is 9°C is approximately 11.07 atm.
b) To calculate the volume of oxygen if the temperature is 26°C and the pressure is 0.095 atm, we can again use the ideal gas law.
Given:
- Temperature (T) = 26°C
- Pressure (P) = 0.095 atm
First, convert the temperature to Kelvin:
T(K) = 26 + 273.15 = 299.15 K
Next, we can assume the number of moles of oxygen (n) remains the same, as it is the same amount of gas. Using the value of n calculated in part a, n = 9.0625 mol.
Rearranging the ideal gas law equation to solve for V:
V = (nRT) / P
Substituting the values:
V = (9.0625 mol × 0.0821 L·atm/(mol·K) × 299.15 K) / 0.095 atm
Calculating the volume (V):
V ≈ 76.95 L
Therefore, the volume of oxygen when the temperature is 26°C and the pressure is 0.095 atm is approximately 76.95 L.
I hope this helps! If you have any more questions, feel free to ask.
a. Use PV = nRT. Don't forget T is in kelvin. n O2 = grams/molar mass
b. use PV = nRT