The pressure of a gas is 1.34 atm at a temperature of 298 K. What will the pressure be if the temperature is increased to 512 K?

Question

Natalie Anton · Accepted Answer

2.30 atm

Pressure is directly proportional to temperature and increases as temperature rises. #P_1# / #T_1# = #P_2# / #T_2# #P_1# = 1.34 atm , #T_1# = 298 K #P_2# = X atm , #T_2# = 512 K X atm / 512 K = 1.34 atm / 298 K We rearrange, 512 K x 1.34 atm = 298 K. X atm 298 K. X atm = 686.08 K atm X atm = 298 K / 686.08 K atm 2.30 atm X atm

Wyatt Adkins · Answer

undefined To find the new pressure, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas:

P1V1 / T1 = P2V2 / T2

Given:
P1 = 1.34 atm
T1 = 298 K
T2 = 512 K

Since we are only interested in the pressure, we can rearrange the equation to solve for P2:

P2 = (P1 * T2) / T1

Plugging in the values:

P2 = (1.34 atm * 512 K) / 298 K
P2 = 2.30 atm

So, the pressure of the gas will be 2.30 atm when the temperature is increased to 512 K.

Wyatt Adkins · Answer

undefined To find the pressure of the gas when the temperature is increased to 512 K, we can use the combined gas law, which relates the pressure, volume, and temperature of a gas:

$$ P_1 \times V_1 / T_1 = P_2 \times V_2 / T_2 $$

Where:
- $ P_1 $ is the initial pressure (1.34 atm)
- $ T_1 $ is the initial temperature (298 K)
- $ P_2 $ is the final pressure (what we want to find)
- $ T_2 $ is the final temperature (512 K)

Since the volume of the gas is not changing, we can simplify the equation to:

$$ P_1 / T_1 = P_2 / T_2 $$

We rearrange the equation to solve for $ P_2 $:

$$ P_2 = P_1 \times (T_2 / T_1) $$

Plugging in the given values:

$$ P_2 = 1.34 \, \text{atm} \times (512 \, \text{K} / 298 \, \text{K}) $$

$$ P_2 = 1.34 \, \text{atm} \times 1.716 $$

$$ P_2 \approx 2.295 \, \text{atm} $$

Therefore, when the temperature is increased to 512 K, the pressure of the gas will be approximately 2.295 atm.