Question

A balloon is floating around outside your window. The temperature outside is 37 ∘C , and the air pressure is 0.700 atm . Your neighbor, who released the balloon, tells you that he filled it with 4.90 moles of gas. What is the volume of gas inside this balloon?

Answer 1

The volume of the balloon can be calculated using the Ideal Gas Law formula PV=nRT. After converting the Celsius temperature to Kelvin and rearranging the formula to solve for volume, the result is approximately 172.66 liters.

Step-by-step explanation:

To find the volume of gas inside the balloon given the number of moles, temperature, and pressure, we can use the Ideal Gas Law, which is PV = nRT. Here, P is the pressure in atmospheres (atm), V is the volume in liters (L), n is the number of moles of gas, R is the ideal gas constant (0.0821 L·atm/(mol·K)), and T is the temperature in Kelvin (K).

First, convert the temperature from degrees Celsius to Kelvin by adding 273.15 to the given temperature. So, T = 37 °C + 273.15 = 310.15 K.

With this information, we can rearrange the equation to solve for V: V = (nRT)/P.

Plugging in the values, we get V = (4.90 moles × 0.0821 L·atm/(mol·K) × 310.15 K) / 0.700 atm, which will give us the volume of the balloon.

Therefore, doing the math, V = (4.90 × 0.0821 × 310.15) / 0.700 ≈ 172.66 liters.

The volume of the balloon filled with 4.90 moles of gas at 0.700 atm and 37 °C is approximately 172.66 liters.