Question

A gas has a pressure of 1.74 atm when the temperature is 237K. The gas is then

heated until the temperature measures 312K. What will be the new pressure? *
2.29 atm
1.32 atm
O 128662.56 atm

Answer 1

`\boxed {\boxed {\sf 1.99 \ atm}}`

Step-by-step 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:

`(P_1)/(T_1)=(P_2)/(T_2)`

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.

`\frac {1.74 \ atm}{273 \ K}=\frac {P_2}{312 \ K}`

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.

`312 \ K *\frac {1.74 \ atm}{273 \ K}=\frac {P_2}{312 \ K}* 312 \ K`

`312 \ K *\frac {1.74 \ atm}{273 \ K}= P_2`

The units of Kelvin (K) will cancel.

`312 \ *\frac {1.74 \ atm}{273 }= P_2`

`1.98857143 \ atm= P_2`

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.

`1.99 \ atm \approx P_2`

The new pressure is approximately 1.99 atmospheres.