balloon is filled with 1.35 atm dimethyl ether gas and 5.25 atm of oxygen gas at 27 C degrees. They react: C2H6O (g) + 3O2 (g) --> 2CO2 (g) + 3H2O(g) The system is allowed to cool back down to 27 degrees Celsius following the reaction. assuming external pressure is still the same (6.60 atm), what is the new volume of the balloon? what is the partial pressure of carbon dioxide in the balloon?

any help please.. we use pv/t ? i don't understand. show work and please explain

To solve this problem, we can use the ideal gas law equation, which is given by:

PV = nRT

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

First, let's find the number of moles of each gas using the ideal gas law equation.

For dimethyl ether (C2H6O):
P1V1 = n1RT1
(1.35 atm) * V1 = n1 * (0.0821 L·atm/mol·K) * (27 + 273) K

For oxygen (O2):
P2V2 = n2RT2
(5.25 atm) * V2 = n2 * (0.0821 L·atm/mol·K) * (27 + 273) K

The balanced chemical equation tells us that 1 mole of dimethyl ether reacts with 3 moles of oxygen. Therefore, the number of moles of dimethyl ether is equal to the number of moles of oxygen divided by 3.

n1 = n2 / 3

Now, let's find the total moles of both gases.

n_total = n1 + n2

Next, we can calculate the new volume of the balloon using the ideal gas law equation after the reaction has occurred.

P_total * V_new = n_total * R * T
(6.60 atm) * V_new = n_total * (0.0821 L·atm/mol·K) * (27 + 273) K

Solve for V_new to find the new volume of the balloon.

V_new = [(n_total * (0.0821 L·atm/mol·K) * (27 + 273) K)] / (6.60 atm)

Now, to find the partial pressure of carbon dioxide (CO2), we'll use the mole ratios from the balanced equation.

According to the balanced equation: C2H6O (g) + 3O2 (g) --> 2CO2 (g) + 3H2O (g)

We can see that 2 moles of CO2 are formed for every 1 mole of C2H6O reacted.

Therefore, the number of moles of CO2 is equal to half the number of moles of dimethyl ether.

n_CO2 = n1 / 2

Finally, we can calculate the partial pressure of CO2.

Partial pressure of CO2 = (n_CO2 * R * T) / V_new

Please plug in the given values into each equation and follow the steps to find the new volume of the balloon and the partial pressure of CO2.