Question

What is the gauge pressure in a 25.0°C car tire containing 3.60 mol of gas in a 30.0-L volume? (b) What will its gauge pressure be if you add 1.00 L of gas originally at atmospheric pressure and 25.0°C? Assume the temperature remains at 25.0°C, and the volume remains constant.

a) 2.53 atm; 3.32 atm
b) 3.32 atm; 2.53 atm
c) 2.10 atm; 2.10 atm
d) 1.90 atm; 1.90 atm

Answer 1

The gauge pressure in the car tire containing 3.60 mol of gas in a 30.0 L volume at 25.0°C is 2.53 atm. Adding 1.00 L of gas originally at atmospheric pressure and 25.0°C will increase the gauge pressure to 3.32 atm.

So The Correct Option is ; a) 2.53 atm; 3.32 atm

Step-by-step explanation:

The gauge pressure in a car tire can be calculated using the ideal gas law equation:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature in Kelvin.

In this case, we are given the volume (30.0 L), the number of moles (3.60 mol), and the temperature (25.0°C). To solve for the pressure, we need to convert the temperature to Kelvin:

T(K) = 25.0°C + 273.15

Now we can substitute the values into the equation:

P(1) * 30.0 L = 3.60 mol * R * (25.0°C + 273.15)

Solving for P(1), we get a gauge pressure of 2.53 atm.

To find the gauge pressure after adding 1.00 L of gas at atmospheric pressure, we need to consider the additional moles of gas. Since the volume remains constant, we can use the ideal gas law equation to find the new pressure:

P(2) * 30.0 L = (3.60 mol + 1.00 L * (1 atm * 30.0 L) / (R * (25.0°C + 273.15)

Solving for P(2), we get a gauge pressure of 3.32 atm.