A 3.80 L cylinder contains 6.83 g of methane, CH4, at a pressure of 3320 mmHg. What is the temp. Of the gas?

I mainly have problems being able to tell which gas law equation I need to use when asked these types of questions and then being able to rearrange the equation to find my answer that I need. If there an easy way to do this or to be able to tell?
Thank you.

To solve this problem, you need to use the ideal gas law equation, which relates the pressure, volume, temperature, and the amount of gas (usually given in moles).

The ideal gas law equation is: PV = nRT

Where:
- P is the pressure of the gas in units of force per unit area (such as mmHg or atm)
- V is the volume of the gas
- n is the number of moles of gas
- R is the ideal gas constant (usually given as 0.0821 L·atm/(mol·K))
- T is the temperature in Kelvin

In this problem, you are given the volume (3.80 L), the pressure (3320 mmHg), and the number of grams of methane (6.83 g). To find the temperature, you need to rearrange the ideal gas law equation and solve for T.

1. Convert the pressure to atm by dividing by 760 mmHg: 3320 mmHg / 760 mmHg/atm = 4.37 atm

2. Convert the mass of methane to moles using its molar mass:
- Molar mass of CH4 = 12.01 g/mol (C) + 4(1.01 g/mol) (4 H) = 16.05 g/mol
- Moles of CH4 = 6.83 g / 16.05 g/mol ≈ 0.426 mol

3. Plug in the values you have into the rearranged ideal gas law equation:
PV = nRT
(4.37 atm)(3.80 L) = (0.426 mol)(0.0821 L·atm/(mol·K))(T)
16.616 L·atm = 0.034896 L·atm/(K·mol) × T

4. Cancel out the units and solve for T:
16.616 L·atm / 0.034896 L·atm/(K·mol) = T
T ≈ 475 K

So the temperature of the gas is approximately 475 Kelvin.

To determine which gas law equation to use, you need to consider which variables are given and which one you are trying to solve for. The ideal gas law equation is the most general equation that can be used when you have the pressure, volume, temperature, and number of moles of gas. If one of these parameters is missing, you may need to use a modified version of the ideal gas law equation, such as Boyle's law, Charles's law, or Avogadro's law.

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

PV = nRT,

where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature.

In this case, you are given the pressure (3320 mmHg), volume (3.80 L), and the amount of methane in grams (6.83 g). To find the temperature, you need to convert the mass of methane to moles using its molar mass. The molar mass of methane (CH4) can be calculated by adding the atomic masses of carbon (12.01 g/mol) and hydrogen (1.01 g/mol) four times:

Molar mass of methane = (12.01 g/mol) + 4 × (1.01 g/mol) = 16.05 g/mol.

Now you can calculate the number of moles (n) of methane in the cylinder using the given mass:

n = mass / molar mass = 6.83 g / 16.05 g/mol.

Let's calculate this value:

n = 6.83 g / 16.05 g/mol = 0.4251 mol.

Now you have all the values needed to apply the ideal gas law equation. Rearranging the equation to solve for T, you get:

T = (PV) / (nR).

Plugging in the given values:

T = (3320 mmHg) × (3.80 L) / (0.4251 mol × R).

The ideal gas constant (R) is typically given in different units, such as L•atm/(mol•K) or J/(mol•K). We'll assume R = 0.0821 L•atm/(mol•K). Plugging in this value:

T = (3320 mmHg) × (3.80 L) / (0.4251 mol × 0.0821 L•atm/(mol•K)).

Now you can calculate T:

T = (3320 mmHg) × (3.80 L) / (0.4251 mol × 0.0821 L•atm/(mol•K)).

Let's calculate this value:

T ≈ 318 K.

Therefore, the temperature of the gas in the cylinder is approximately 318 K.

If you have two sets of conditions, the easy gas law to use is the

(P1V1/T1) = (P2V2/T2)

If you don't have two sets of data you almost certainly must use PV = nRT. Many times, and this problem is one of them, the problem gives grams so you calculate mols = n = grams/molar mass.

Also,if you mean by "rearranging the equation to find my answer" as rearranging the equation FIRST, I wouldn't do that. I would substitute into the equation you want (either of the two equations above), then rearrange the numbers to solve for the unknown.
For this problem you want PV = nRT.
P must be in atm (mmHg/760), n = mols = grams/molar mass, when you solve for T the answer will be in kelvin.