a vessel contains 12 gm of methane gas at t degree celcius temp. and 1 atm. pressure. when the temp. is increased by 10 degree celcius at the same volume, the pressure increases by 10%. calculate the volume and initial temp.

First, note the correct spelling of celsius.

I would do something like this.
You know 12 g CH4 = 12/16 = 0.75 mole CH4. Then use PV = nRT
1atm*V = 0.75*0.08206*(273+t)

Then when t increases by 10 C, p increases by 10%; therefore, use PV = nRT again, this time P =1.1 atm and T is (273+t+10) and it would look like this.
1.1atm*V = 0.75*0.08206*(273+t+10).
The problem tells you that both are at the same volume (but not what the volume is), so set the two equal.
0.75*0.08206*(273+10) = [0.75*0.08206*(273+t+10)]/1.1
and solve for t, the only unknown. Then use PV = nRT and the original numbers to solve for V. Check my thinking. Check for typos. As a check I substituted the value for V and 1.1 for P and solved for the new T and, indeed, obtained 10 higher t.

thank you so much drbob222. u are a genius. could you check out my physics questions too?

To solve this problem, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

Step 1: Convert the temperature from Celsius to Kelvin.
To convert from Celsius to Kelvin, we use the formula: T(K) = T(°C) + 273.15.

Given temperature T (initial) = t degrees Celsius, so T(initial) = t + 273.15.
Temperature T (final) = t + 10 degrees Celsius, so T(final) = (t + 10) + 273.15.

Step 2: Determine the number of moles of methane gas.
Since the only information given is the mass of methane gas, we need to convert the mass to moles using the molar mass of methane (CH4).

The molar mass of methane is:
Molar mass of C = 12.01 g/mol
Molar mass of H = 1.01 g/mol
So, molar mass of CH4 = (12.01 g/mol) + (4 * 1.01 g/mol) = 16.05 g/mol.

Given mass of methane gas = 12 g, so:
Number of moles of methane gas = mass / molar mass = 12 g / 16.05 g/mol.

Step 3: Calculate the initial volume using the ideal gas law equation.
Using the ideal gas law equation PV = nRT, we need to rearrange it to solve for V.
V(initial) = (nRT(initial)) / P.

We know:
P (initial) = 1 atm.
V (initial) = unknown.
n = (mass of gas) / (molar mass of gas).
R is the gas constant (0.0821 L·atm/mol·K).

V(initial) = [(mass / molar mass) * R * T(initial)] / P.

Step 4: Calculate the final pressure.
Since the volume is constant and the pressure increases by 10%, we can say:
P(final) = P(initial) + (10/100) * P(initial).

Step 5: Calculate the final volume using Boyle's Law.
Boyle's Law states that for a fixed amount of gas at a constant temperature, the pressure and volume are inversely proportional.
P(initial) * V(initial) = P(final) * V(final).

Since the volume increases by 10% but the pressure increases by 10%, we can say:
V(final) = (1 / 1.1) * V(initial).

Now, you have all the equations needed to solve the problem. Simply substitute the known values into the equations and solve for the unknowns (V(initial) and t).