The adult blue whale has a lung capacity of 5.0*10^3L. Calculate the mass of air (assume an average molar mass 28.98 g/mol ) contained in an adult blue whale’s lungs at 0.3 degrees Celcius and 1.10 atm., assuming the air behaves ideally.
Calculate the number of molecules in a deep breath of air whose volume is 2.30 Liters at body temperature, 36 degrees Celcius, and a pressure of 740 torr .
Note the correct spelling of celsius.
Use PV = nRT and solve for n = number of moles. Then n = grams/molar mass and solve for grams.
Do the same for the second part, solve for n = number of moles. Then convert moles to # molecules remembering that there are 6.02E23 molecules in 1 mole.
0.089g
6.9g
To calculate the mass of air in an adult blue whale's lungs, 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 ideal gas constant, and T is the temperature.
First, we need to convert the pressure from atm to kPa, as the ideal gas constant (R) is in units of kPa·L/mol·K.
Given:
Lung capacity (V) = 5.0 * 10^3 L
Pressure (P) = 1.10 atm
Temperature (T) = 0.3 °C, which needs to be converted to Kelvin (K) by adding 273.15.
Molar mass (M) = 28.98 g/mol
Step 1: Convert the pressure from atm to kPa:
1 atm = 101.325 kPa (approximately)
1.10 atm * 101.325 kPa/atm = 111.4575 kPa
Step 2: Convert the temperature to Kelvin:
Temperature in Kelvin = 0.3 °C + 273.15 = 273.45 K
Step 3: Calculate the number of moles (n):
Using the ideal gas law equation, rearranged to solve for n:
n = PV / RT
n = (111.4575 kPa) * (5.0 * 10^3 L) / [(0.0821 kPa·L/mol·K) * (273.45 K)]
Note: The ideal gas constant, R, is approximately 0.0821 kPa·L/mol·K.
Step 4: Calculate the mass of air:
Mass (m) = n * M
m = n * M = [(111.4575 kPa) * (5.0 * 10^3 L) / [(0.0821 kPa·L/mol·K) * (273.45 K)]] * (28.98 g/mol)
Thus, we can calculate the mass of air in the blue whale's lungs.
For the second question regarding the number of molecules in a deep breath of air:
Given:
Volume (V) = 2.30 L
Pressure (P) = 740 torr
Temperature (T) = 36 °C, which needs to be converted to Kelvin (K) by adding 273.15.
Step 1: Convert the pressure from torr to atm:
1 torr = 1/760 atm
740 torr * (1/760 atm/torr) = 0.974 atm
Step 2: Convert the temperature to Kelvin:
Temperature in Kelvin = 36 °C + 273.15 = 309.15 K
Step 3: Calculate the number of moles (n):
Using the ideal gas law equation:
n = PV / RT
n = (0.974 atm) * (2.30 L) / [(0.0821 atm·L/mol·K) * (309.15 K)]
Note: The ideal gas constant, R, is approximately 0.0821 atm·L/mol·K.
Step 4: Calculate the number of molecules:
Number of molecules = n * Avogadro's number
The Avogadro's number is approximately 6.022 x 10^23 molecules/mol.
Thus, we can calculate the number of molecules in a deep breath of air.