Certainly! Let's solve this problem step-by-step.
We are given:
1. Initial volume of the gas ([tex]\( V_1 \)[/tex]) = 228 cm³
2. Initial pressure ([tex]\( P_1 \)[/tex]) = 750 mmHg
3. Final pressure ([tex]\( P_2 \)[/tex]) at atmospheric pressure = 760 mmHg (standard value)
We need to find the final volume ([tex]\( V_2 \)[/tex]) at the atmospheric pressure.
To solve this, we will use Boyle's Law, which states that the product of the pressure and volume of a gas is constant as long as the temperature remains unchanged. Mathematically, Boyle's Law can be expressed as:
[tex]\[ P_1 \cdot V_1 = P_2 \cdot V_2 \][/tex]
From the equation above, we can solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{P_1 \cdot V_1}{P_2} \][/tex]
Now, let's substitute the given values into the equation:
[tex]\[ V_2 = \frac{750 \, \text{mmHg} \cdot 228 \, \text{cm}^3}{760 \, \text{mmHg}} \][/tex]
Upon simplifying this expression, the mmHg units will cancel out, leaving us with:
[tex]\[ V_2 = \frac{750 \cdot 228}{760} \][/tex]
After performing the division, we get:
[tex]\[ V_2 = 225 \, \text{cm}^3 \][/tex]
Thus, the volume of the gas at atmospheric pressure (760 mmHg) is [tex]\( 225 \, \text{cm}^3 \)[/tex].
