i reallly need help with combining the gas laws. here are a few questions i am struggling with if anyone could please help!

1. A steel container holds 750.L of O2 gas at STP.
a) how many moles of O2 does the container hold?
b)how many grams of O2 does the container hold?
c) if the pressure were reduced by removal of gas until it was 380.mm Hg, what mass of tha gas would remain in the tank?

2. Given 100.mL of a gas at 22 degrees celcius and 380 mm Hg, what would the volume be at STP?

3. The volume of a dry gas originally at STP was recorded as 488.8mL. What volume would the same gas occupy when subjected to a pressure of 1.00 x 10^4 kPa and temperature of -245 degrees celcius.

4. the mass of 15.0 mL of a gas at 500. kPa of pressure and a temperature of -53 degrees celcius is 8.35 x 10^-3g.
a) what is the density of this gas at these conditions?
b) what is the density of this gas at STP conditions?

Sure! I can help you with combining the gas laws. To solve these problems, we'll need to use a combination of the ideal gas law equation, as well as the relationships between pressure, volume, moles, and temperature in a gas.

Let's break down each question step by step:

1. a) To find the number of moles of O2 in the container, we can use the ideal gas law equation: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

At STP (standard temperature and pressure), the pressure is 1 atm and the temperature is 273.15 K. We can plug in these values:

P = 1 atm
V = 750 L

Rearranging the ideal gas law equation to solve for n, we get:

n = PV / RT

Substituting the given values, we have:

n = (1 atm) * (750 L) / (0.0821 L·atm/mol·K) * (273.15 K)

Simplifying this equation will give you the number of moles of O2 in the container.

b) To find the mass of O2 in the container, we need to convert the moles to grams using the molar mass of O2. The molar mass of O2 is approximately 32 g/mol.

You can calculate the mass by multiplying the number of moles obtained in part a) by the molar mass of O2.

c) To find the mass of the gas remaining in the tank when the pressure is reduced to 380 mm Hg, we can use the combined gas law. The combined gas law combines Boyle's law (PV = constant), Charles's law (V/T = constant), and Gay-Lussac's law (P/T = constant).

The formula for the combined gas law is:

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

You can plug in the given values for P1, V1, T1, and the new pressure P2, to solve for V2. The volume V2 will give you the remaining volume of the gas in the container.

Once you have the remaining volume, you can use the ideal gas law to calculate the new number of moles of O2 using the new pressure (380 mm Hg), volume, and temperature (STP).

Finally, you can find the mass of the remaining gas by multiplying the new number of moles by the molar mass of O2.

2. To find the volume of the gas at STP, we can use the combined gas law again. Now we are given the initial volume V1, temperature T1 (22 degrees Celsius), and pressure P1 (380 mm Hg). We want to find the volume at STP, so the new pressure P2 is 1 atm, and the new temperature T2 is 273.15 K (STP).

Using the combined gas law equation, you can solve for the new volume (V2) by plugging in the given values and solving for V2.

3. To find the new volume of the gas when subjected to a pressure of 1.00 x 10^4 kPa and a temperature of -245 degrees Celsius, we can use the combined gas law once again. The initial pressure P1 is 1 atm, the initial volume V1 is given (488.8 mL), and the initial temperature T1 is 273.15 K (STP).

Plug in the given values for P1, V1, T1, and the new pressure P2 and temperature T2 to solve for V2.

4. a) To find the density of the gas at the given conditions (pressure, temperature, and mass), we can use the ideal gas law equation. The ideal gas law equation can be rearranged to solve for density:

density = (mass of gas) / (volume of gas)

You can calculate the volume by using the combined gas law equation and plugging in the given values for pressure, temperature, and the initial volume (15.0 mL in this case). Once you have the volume, you can substitute the given mass of the gas to calculate the density.

b) To find the density of the gas at STP conditions, you can use the molar mass of the gas and the ideal gas law equation. Since STP conditions have a pressure of 1 atm, a temperature of 273.15 K, and the volume is unknown, we can use the ideal gas law equation and rearrange it to solve for density.

That's it! By using these explanations and the formulas, you should be able to solve the problems on your own. Good luck!