A mouse is placed in a sealed chamber with air at 755.0 torr. This chamber is equipped with enough solid KOH to absorb any CO2 and H2O produced by the mouse. The gas volume in this chamber is measured to be exactly 1.70 L, the temperature is held constant at 305 K. After two hours the pressure inside the bottle falls to 715.1 torr. What mass of oxygen has the mouse consumed?

Try this.

n initial = PV/RT
Solve for n initial.

Then redo at the lower pressure and solve for n final.

The delta n = n final- n initial =
mols O2 used.
Then grams = mols x molar mass.

Well, it seems like the mouse has been quite the party animal in that sealed chamber. It looks like it's been inhaling some oxygen and exhaling some CO2! Let's crunch some numbers to figure out how much oxygen it consumed.

Let's start by using the ideal gas law: PV = nRT. In this case, since the temperature and volume are constant, we can simplify it to P1/n1 = P2/n2.

We're given the initial pressure, P1 = 755.0 torr, and the final pressure, P2 = 715.1 torr. We want to find the change in moles of gas, so we can rewrite the equation as P1/V = n1/RT1 and P2/V = n2/RT2.

The volume, V, is given as 1.70 L, and the temperature, T, is 305 K. So let's plug in the values and solve for the moles of gas:

n1 = (P1 * V) / (R * T1)
n1 = (755.0 torr * 1.70 L) / (0.0821 L.atm/mol.K * 305 K)
n1 = 0.04478 mol

n2 = (P2 * V) / (R * T2)
n2 = (715.1 torr * 1.70 L) / (0.0821 L.atm/mol.K * 305 K)
n2 = 0.04249 mol

Now, to find the change in moles, we subtract n2 from n1:

∆n = n1 - n2
∆n = 0.04478 mol - 0.04249 mol
∆n = 0.00229 mol

Since 1 mole of O2 is consumed for every 2 moles of CO2 produced, we divide ∆n by 2 to find the amount of O2 consumed:

∆n(O2) = ∆n / 2
∆n(O2) = 0.00229 mol / 2
∆n(O2) = 0.00114 mol

Now, we just need to find the mass of O2 consumed. The molar mass of O2 is approximately 32 g/mol, so:

Mass(O2) = ∆n(O2) * Molar mass(O2)
Mass(O2) = 0.00114 mol * 32 g/mol
Mass(O2) = 0.03648 g

Therefore, the mouse has consumed approximately 0.03648 grams of oxygen. It seems like this mouse knows how to breathe in style!

To find the mass of oxygen consumed by the mouse, we can use the ideal gas law equation:

PV = nRT

Where:
P = pressure
V = volume
n = number of moles
R = gas constant
T = temperature

We can rearrange this equation to solve for the number of moles of gas:

n = PV / RT

First, we need to calculate the initial number of moles of gas in the chamber.

n1 = (P1 * V) / (R * T)

Where:
P1 = initial pressure = 755.0 torr
V = volume = 1.70 L
R = 0.0821 L × atm / (mol × K) (the ideal gas constant)
T = temperature = 305 K

Calculating n1:

n1 = (755.0 torr * 1.70 L) / (0.0821 L × atm / (mol × K) * 305 K)

Now, we can calculate the final number of moles of gas in the chamber.

n2 = (P2 * V) / (R * T)

Where:
P2 = final pressure = 715.1 torr
V = volume = 1.70 L
R = 0.0821 L × atm / (mol × K) (the ideal gas constant)
T = temperature = 305 K

Calculating n2:

n2 = (715.1 torr * 1.70 L) / (0.0821 L × atm / (mol × K) * 305 K)

The difference between n1 and n2 will give us the number of moles of oxygen consumed by the mouse.

nO2_consumed = n1 - n2

Finally, we can calculate the mass of oxygen consumed using the molar mass of oxygen (32.0 g/mol).

mass_O2_consumed = nO2_consumed * molar mass_O2

Now, let's calculate all the values.

R = 0.0821 L × atm / (mol × K) (the ideal gas constant)
molar mass_O2 = 32.0 g/mol

n1 = (755.0 torr * 1.70 L) / (0.0821 L × atm / (mol × K) * 305 K)
n2 = (715.1 torr * 1.70 L) / (0.0821 L × atm / (mol × K) * 305 K)
nO2_consumed = n1 - n2
mass_O2_consumed = nO2_consumed * molar mass_O2

After calculating all these values, you will have the mass of oxygen consumed by the mouse.

To calculate the mass of oxygen consumed by the mouse, we need to use the ideal gas law equation. The ideal gas law equation is:

PV = nRT

Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature (in Kelvin)

First, we need to convert the pressure from torr to atm. We can use the conversion factor: 1 atm = 760 torr.

Initial pressure (Pi): 755.0 torr = 0.9947 atm
Final pressure (Pf): 715.1 torr = 0.9416 atm

Now we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

Since the temperature (T) is constant, we can simplify the equation:

n = (PV) / (RT)

Using the initial pressure (Pi) and volume (V), we can calculate the initial number of moles (ni):

ni = (Pi * V) / (RT)

Using the final pressure (Pf) and volume (V), we can calculate the final number of moles (nf):

nf = (Pf * V) / (RT)

The difference between the initial and final number of moles will give us the number of moles consumed by the mouse:

Δn = ni - nf

Finally, to calculate the mass of oxygen consumed, we need to multiply the number of moles (Δn) by the molar mass of oxygen (32.00 g/mol).

Molar mass of oxygen (O2) = 32.00 g/mol

Mass of oxygen consumed = Δn * (molar mass of oxygen)

Therefore, to find the mass of oxygen consumed by the mouse, you need to follow these steps:

1. Convert the initial and final pressures from torr to atm.
2. Calculate the initial and final number of moles using the ideal gas law equation.
3. Find the difference in moles (Δn).
4. Multiply Δn by the molar mass of oxygen (32.00 g/mol) to get the mass of oxygen consumed.