A 3.80 L cylinder contains 6.83g of methane, CH4, at a pressure of 3320 mmHg. What is the temperature of the gas?
I know you use the formula PV= nRT, but I can't seem to get two sides equal each other, thus having the wrong temp. My guess is that I have to change mmHg to a different unit.
If you are using P in anything other than atm, that's not right. 3320/760 = atm.
V must be in L and T will be in kelvin.
To solve this problem, you need to use the ideal gas law equation, which is PV = nRT.
Let's start by breaking down the given information:
- Volume (V) = 3.80 L
- Pressure (P) = 3320 mmHg
- Amount of substance (n) = unknown
- Ideal gas constant (R) = known value: 0.0821 L·atm/(mol·K)
You correctly identified that one potential issue is the different units for pressure. In this case, we need to convert the pressure from mmHg to atm since the ideal gas constant has units that are compatible with atm.
To convert mmHg to atm, you can use the conversion factor: 1 atm = 760 mmHg.
So, the pressure in atm is: 3320 mmHg ÷ 760 mmHg/atm = 4.37 atm.
Now let's proceed with the formula PV = nRT:
(4.37 atm) × (3.80 L) = n × (0.0821 L·atm/(mol·K)) × T
To solve for the temperature (T), we need to know the number of moles of methane (n). We can calculate this using the molecular weight of methane (CH4). Its molecular weight is approximately 16 g/mol.
Given that the mass of methane (CH4) is 6.83 g, we can calculate the number of moles:
n = mass / molecular weight
n = 6.83 g / 16 g/mol
n ≈ 0.4269 mol
Now we can substitute all the known values into the equation:
(4.37 atm) × (3.80 L) = (0.4269 mol) × (0.0821 L·atm/(mol·K)) × T
Simplifying this equation gives:
16.636 atm·L = 0.0349869 mol·L·atm·K × T
Dividing both sides by 0.0349869 mol·L·atm·K gives:
T = (16.636 atm·L) / (0.0349869 mol·L·atm·K)
T ≈ 474.36 K
Therefore, the temperature of the gas is approximately 474.36 K.
To solve this problem, you're on the right track using the ideal gas law equation PV = nRT. However, you don't necessarily need to convert mmHg to a different unit in this case.
Here's how you can solve it step by step:
Step 1: Convert the pressure to atm.
The conversion factor is 1 atm = 760 mmHg.
So, the pressure in atm is:
3320 mmHg x (1 atm / 760 mmHg) = 4.37 atm
Step 2: Convert the mass of methane to moles.
To do this, use the molar mass of methane (CH4):
1 mol CH4 = 12.01 g (C) + 4(1.01 g) (4 H) = 16.04 g
The number of moles of methane is:
6.83 g CH4 x (1 mol / 16.04 g) = 0.426 mol
Step 3: Substitute the values into the ideal gas law equation and solve for temperature (T).
PV = nRT
4.37 atm x 3.80 L = 0.426 mol x R (gas constant) x T
Simplifying, we have:
16.576 L atm = 0.426 mol x R x T
Now, you need the value for the gas constant, R. The most common value for R is 0.0821 L atm / (K mol).
Step 4: Rearrange the equation to solve for temperature (T).
T = (16.576 L atm) / (0.426 mol x 0.0821 L atm / (K mol))
Simplifying, we have:
T = 468.4 K
So, the temperature of the gas is approximately 468.4 K.