how to solve for a 28.4 L sample of methane gas is heated from 35.0° C to 76.0° C. The initial pressure of the gas is 1.00 atm at 35.0° C. Assuming constant volume, what is the final pressure of the gas?

OK, I did the following:

P₁ = 28.4 L P₂ = ?
T₁ = 41.0◦C T₂ = 35.0◦C
+273.15K= +273.15 K=
314.2K 308.2K

P₁T₁ = P₂
T₂

(28.4 L)(314.2 K) = 29.0 L
(308.2 K)

Do my answer looks correct which is 29.0 L

The question is asking for pressure so 29.0 L cannot be correct.

P1/T1 =P2/T2 where P is the pressure and T is the temperature in kelvin.

35.0C is (273.15+35.0) K
=308.15 K

76.0C is (273.15+76.0) K
=349.15 K

P1=1.00 atm

so

1.00 atm / 308.15 K
= P2 / 349.15 K

P2 = 1.133 atm

which is 1.13 atm to 3 sig figs (the starting pressure is to 3 sig figs)

Actually, your approach to solving the problem is incorrect. Let me help you understand the correct steps.

To solve for the final pressure of the gas, you need to use the ideal gas law equation, which states:

PV = nRT

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

In this case, you're assuming constant volume, so the equation simplifies to:

P₁/T₁ = P₂/T₂

where P₁ and T₁ are the initial pressure and temperature, and P₂ and T₂ are the final pressure and temperature.

Here are the steps to solve the problem correctly:

1. Convert the temperatures to Kelvin:
T₁ = 35.0°C + 273.15 = 308.15 K
T₂ = 76.0°C + 273.15 = 349.15 K

2. Substitute the given values into the equation:
P₁ / T₁ = P₂ / T₂

3. Solve for P₂ by rearranging the equation:
P₂ = P₁ * (T₂ / T₁)

4. Substitute the known values into the equation:
P₂ = 1.00 atm * (349.15 K / 308.15 K)

5. Calculate the final pressure:
P₂ = 1.13 atm (rounded to two decimal places)

So, the correct final pressure of the gas is 1.13 atm, not 29.0 L as you suggested in your answer.