Calculate the number of molecules in a deep breath of air whose volume is 2.68 L at body temperature, 37°C, and a pressure of 743 torr
(b) The adult blue whale has a lung capacity of 5.0 103 L. Calculate the mass of air (assume an average molar mass 28.98 g/mol) contained in an adult blue whale's lungs at 0.0°C and 1.00 atm, assuming the air behaves ideally.
how do i do these?
(a)
V=2.68 L = 0.00268 m³,
t=37°C => T=310 K,
p=743 torr =99058.246 Pa
R=8.31 J/mol
pV=nRT
n= pV/RT = 99058.246•0.00268/8.31•310 =0.1 mol
N= n•N₀=0.1•6.02•10²³=6.02•10²² molecules
(b)
V=5•10³ L=5 m³
μ=28.98 g/mol=28.98•10⁻³ kg/mol
t=0℃ =273 K
p =1 atm = 101325 Pa
pV=mRT/μ
m=pVμ/RT=101325•5• 28.98•10⁻³/8.31•273 =6.47 kg
To solve these questions, we need to use the ideal gas law equation, which is given by:
PV = nRT
Where:
- P is the pressure of the gas (in atm)
- V is the volume of the gas (in liters)
- n is the number of moles of the gas
- R is the ideal gas constant (0.0821 L·atm/(mol·K))
- T is the temperature of the gas (in Kelvin)
To find the number of molecules (n) in a given volume of gas, we can use the Avogadro's law, which states that 1 mole of any substance contains 6.022 x 10^23 particles (Avogadro's number).
Now let's solve each question step by step:
(a) Calculate the number of molecules in a deep breath of air:
1. Convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 37°C + 273.15 = 310.15 K
2. Convert the pressure from torr to atm:
P(atm) = P(torr) / 760
P = 743 torr / 760 = 0.976 atm
3. Substitute the given values into the ideal gas law equation:
PV = nRT
n = (PV) / (RT)
= (0.976 atm * 2.68 L) / (0.0821 L·atm/(mol·K) * 310.15 K)
= 0.1129 moles of air
4. Now, multiply the number of moles by Avogadro's number to get the number of molecules:
Number of molecules = 0.1129 moles * 6.022 x 10^23 molecules/mole
(b) Calculate the mass of air in an adult blue whale's lungs:
1. Convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T = 0°C + 273.15 = 273.15 K
2. Convert the given pressure from atm to torr:
P(torr) = P(atm) * 760
P = 1.00 atm * 760 torr/atm = 760 torr
3. Substitute the given values into the ideal gas law equation:
PV = nRT
n = (PV) / (RT)
= (760 torr * 5000 L) / (0.0821 L·atm/(mol·K) * 273.15 K)
= 166.7 moles of air
4. Multiply the number of moles by the molar mass to get the mass of air:
Mass of air = 166.7 moles * 28.98 g/mol
These calculations should give you the answers to both questions. Make sure to double-check the calculations and units to ensure accuracy.