please help me !!

Question

1) A 728 mL gas sample at STP is compressed to a volume of 219 mL, and the temperature is increased to 30◦C. What is the new pressure of the gas in Pa? Answer in units of Pa.

2)A sample of oxygen is collected in a 268 mL container over water at 15◦C, and the barometer reads 756 torr. What volume would the dry gas occupy at 787 torr and 15◦C? Water’s partial pressure at 15◦C is 12.8 torr. Answer in units of mL.

3)Before a trip from New York to Boston, the pressure in an automobile tire is 1.9 atm at 284 K. At the end of the trip, the pressure gauge reads 1.89 atm. What is the new Celsius temperature of the air inside the tire? (Assume tires with constant volume.) Answer in units of ◦C.

4)A helium balloon has a volume of 18.2 L when the pressure is 1.176 atm and the temperature is 19 ◦C. The balloon is cooled at a constant pressure until the temperature is −12◦C. What is the volume of the balloon at this stage?

5)A gas occupying 44 mL at standard conditions is heated to 18◦C while the pressure is reduced to 0.85737 atm. What is the new volume occupied by the gas? Answer in units of mL.

Answer 1

I can help you set up these problems so you can find the answers on your own.

1) STP (standard temperature and pressure) = 0 Degrees Celsius (273.15 Kelvin, to convert to Kelvin you add 273.15 to the temperature in celsius) and 1 atm (can also be expressed as 14.68 psi, 760 mmHg, and 101.325 kPa).

Ideal Gas Law: PV = nRT where P = pressure, V = volume (in Liters), n = moles of gas, R = Ideal gas constant (you can find all of the values for R on google, be sure to use the value that has the same pressure units as the units that are given in the problem), and T = Temperature in Kelvin.

The ideal gas law can be rewritten to relate pressure, volume, and temperature as follows:

P₁V₁/T₁ = P₂V₂/T₂ (the reason why I left out n and R is because R is a constant, and the moles of gas are not changing, only the temperatures, pressures, and volumes are. So we do not need to include n and R in our equation)

In this problem, you are given the values for V1, P1, T1, V2, and T2, and you are being asked to solve for P2. (V = volume, P = pressure, T = temperature (kelvin), 1 denotes the initial value for each variable, 2 denotes the final value for each variable).

Plug in the known values for each variable into the modified ideal gas law equation that I provided to solve for P2. Be sure to check your units (if you use the value of P provided for STP, be sure to convert from kPa to Pa.)

2) For this problem, you have to utilize Dalton's Law of Partial Pressures.

P_Total = P_oxygen + P_Water

You are given the pressure of water at 15 degrees, and the pressure of oxygen (756 torr), use these two values to calculate P_Total

Again using the ideal gas law: PV = nRT, we are going to rewrite an equation to solve for the unknown volume.

In this problem, only pressure and volume are changing. R is a constant, n, the moles of gas remain the same, and T remains the same (15 degrees C), so R, T, and n are not needed in our new equation.

So you will use the equation: P₁V₁ = P₂V₂ and solve for the unknown volume (Boyle's Law).

3) Tires have constant volume, but the variables that are changing are pressure and temperature.

Rewrite the ideal gas law (PV = nRT), to relate pressure and temperature (remember that R, n, and V are all constants in this scenario, so you do not need to worry about these values).

Your new equation: P₁/T₁ = P₂/T₂ , use the given values to solve for T. Remember when carrying out your calculations, you must use the temperature value in Kelvin for T1, and you will need to convert T2 from kelvin to celsius in order to get your answer.

4) Pressure is constant, but volume and temperature are changing.

Rewrite the ideal gas law: V₁/T₁ = V₂/T₂ and solve for V₂.

5) Pressure, volume and temperature are all changing. You are going to use the same formula that I provided from question 1: (P₁V₁/T₁ = P₂V₂/T₂) to solve for the final temperature (T₂).

Important things to remember when carrying out these calculations:

-You must always use the temperature in Kelvin when carrying out your calculations. This is because these equations rely on absolute temperature (kelvin is a scale of absolute temperature, celsius is not)

-Volume should always be expressed in liters when carrying out your calculations (be sure to convert your final answer to mL if the question asks).

-Be sure to use the correct metric prefixes (ie, always convert kPa to Pa).

I hope this helps! Please comment with any feedback in case you have any other questions or need me to clarify anything.