Answer:
[tex]\boxed {\boxed {\sf 6.4 \ atm}}[/tex]
Explanation:
We are asked to find the pressure of a gas in a can given a change in temperature. We will use Gay-Lussac's Law, which states the pressure of a gas is directly proportional to the temperature. The formula for this law is:
[tex]\frac {P_1}{T_1}= \frac {P_2}{T_2}[/tex]
Initially, the gas in the aerosol can has a pressure of 3.10 atmospheres at a temperature of 25 degrees Celsius.
[tex]\frac { 3.10 \ atm}{25 \textdegree C}=\frac{P_2}{T_2}[/tex]
The temperature is increased to 52 degrees Celsius, but the pressure is unknown.
[tex]\frac { 3.10 \ atm}{25 \textdegree C}=\frac{P_2}{52 \textdegree C}[/tex]
We are solving for the new pressure, so we must isolate the variable [tex]P_2[/tex]. It is being divided by 52 degrees Celsius. The inverse operation of division is multiplication, so we multiply both sides of the equation by 52 °C.
[tex]52 \textdegree C *\frac { 3.10 \ atm}{25 \textdegree C}=\frac{P_2}{52 \textdegree C} * 52 \textdegree C[/tex]
[tex]52 \textdegree C *\frac { 3.10 \ atm}{25 \textdegree C}=P_2[/tex]
The units of degrees Celsius cancel.
[tex]52 *\frac { 3.10 \ atm}{25}=P_2[/tex]
[tex]52 *0.124 \ atm = P_2[/tex]
[tex]6.448 \ atm = P_2[/tex]
The original values of pressure and temperature have 2 and 3 significant figures. Our answer must be rounded to the least number of sig figs, which is 2. For the number we calculated, that is the tenths place. The 4 in the hundredth place tells us to leave the 4 in the tenths place.
[tex]6.4 \ atm \approx P_2[/tex]
The gas pressure in the can at 52 degrees Celsius is approximately 6.4 atmospheres.
