A very flexible helium-filled balloon is released from the ground into the air at 20degree C The initial volume of the balloon is 5.00L , and the pressure is 760mmHg. . The balloon ascends to an altitude of 20Km , where the pressure is 76.0mmHg and the temperature is -50degree C What is the new volume,V2 , of the balloon in liters, assuming it doesn't break or leak? plss don't know how to solve this pls if you show me how to do it plsss. thank you

To solve this problem, we can use the ideal gas law, which states that 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.

First, let's convert the initial temperature of 20 degrees Celsius to Kelvin by adding 273.15:
Initial temperature (T1) = 20°C + 273.15 = 293.15 K

Next, we can calculate the number of moles (n) of gas using the initial pressure and volume, along with the ideal gas law. Rearranging the formula, we have n = PV / RT. Since R is a constant, we can find the value of n using the given values:
n = (760 mmHg * 5.00 L) / (0.0821 L·atm/mol·K * 293.15 K)
n ≈ 1.009 mol

Now, we can use the value of n and the new conditions at an altitude of 20 km to find the new volume (V2). However, since the given pressure is in mmHg, we need to convert it to atm by dividing by 760.
New pressure (P2) = 76.0 mmHg / 760 mmHg/atm = 0.1 atm

Next, let's convert the new temperature of -50 degrees Celsius to Kelvin:
New temperature (T2) = -50°C + 273.15 = 223.15 K

Now, we can use the ideal gas law with the new pressure, temperature, and the known number of moles to find the new volume:
V2 = (n * R * T2) / P2
V2 = (1.009 mol * 0.0821 L·atm/mol·K * 223.15 K) / 0.1 atm
V2 ≈ 18.06 L

Therefore, the new volume (V2) of the balloon at an altitude of 20 km is approximately 18.06 liters.

To solve this problem, we can use the combined gas law equation:

(P1 * V1) / (T1) = (P2 * V2) / (T2)

Where:
P1 = initial pressure in mmHg
V1 = initial volume in liters
T1 = initial temperature in Kelvin
P2 = final pressure in mmHg
V2 = final volume in liters (what we need to find)
T2 = final temperature in Kelvin

First, let's convert the temperatures from Celsius to Kelvin:

Initial temperature, T1 = 20°C + 273.15 = 293.15 K
Final temperature, T2 = -50°C + 273.15 = 223.15 K

Next, let's substitute the given values into the equation:

(760 mmHg * 5.00 L) / (293.15 K) = (76.0 mmHg * V2) / (223.15 K)

Now, let's solve for V2:

V2 = (760 mmHg * 5.00 L * 223.15 K) / (76.0 mmHg * 293.15 K)
V2 = (1115756.00 mmHg*L*K) / (22312.40 mmHg*K)
V2 = 50.03 L

Therefore, the new volume, V2, of the balloon at an altitude of 20 km is approximately 50.03 liters.

(P1V1/T1) = (P2V2/T2)

T1 and T2 must be in kelvin.