Answer:
[tex]\boxed {\boxed {\sf 1.99 \ atm}}[/tex]
Explanation:
We are finding the pressure with a change in temperature, so we should use Gay Lussac's Law. This states that the pressure is directly proportional to the temperature. The formula is:
[tex]\frac{P_1}{T_1}=\frac{P_2}{T_2}[/tex]
The original pressure is 1.74 atmospheres and a temperature of 273 Kelvins. When the gas is heated the new temperature is 312 Kelvins, but the new pressure is unknown. Substitute all the known values into the formula.
[tex]\frac {1.74 \ atm}{273 \ K}=\frac {P_2}{312 \ K}[/tex]
Since we are solving for the new pressure, we need to isolate the variable P₂. It is being divided by 312 Kelvin and the inverse of division is multiplication. Multiply both sides by 312 K.
[tex]312 \ K *\frac {1.74 \ atm}{273 \ K}=\frac {P_2}{312 \ K}* 312 \ K[/tex]
[tex]312 \ K *\frac {1.74 \ atm}{273 \ K}= P_2[/tex]
The units of Kelvin (K) will cancel.
[tex]312 \ *\frac {1.74 \ atm}{273 }= P_2[/tex]
[tex]1.98857143 \ atm= P_2[/tex]
The original measurements have 3 significant figures, so our answer must have the same. For the number we found, that is the hundredth place.
The 8 in the thousandth place tells us to round 8 in the hundredth place up to a 9.
[tex]1.99 \ atm \approx P_2[/tex]
The new pressure is approximately 1.99 atmospheres.
