A sample of argon gas occupies a volume of 295ml at 36 C. What volume will the gas occupy at 55 assuming constant pressure?
313
55 WHAT units?
(V1/T1) = (V2/T2)
Remember T is in kelvin.
To solve this problem, we can use the combined gas law, which states that the product of pressure and volume is directly proportional to the product of temperature and the number of moles of gas.
The formula for the combined gas law is:
(P1 * V1) / T1 = (P2 * V2) / T2
Given:
P1 = P2 (constant pressure)
V1 = 295 ml
T1 = 36 °C (convert to Kelvin by adding 273.15)
T2 = 55 °C (convert to Kelvin by adding 273.15)
V2 = ? (volume at 55 °C)
Let's substitute the values into the equation and solve for V2:
(P1 * V1) / T1 = (P2 * V2) / T2
(P1 * V1 * T2) / (T1 * P2) = V2
Since the pressure is constant, P1 / P2 = 1. Therefore, we can simplify the equation to:
(V1 * T2) / T1 = V2
Now, let's calculate the volume at 55 °C:
V2 = (V1 * T2) / T1
V2 = (295 ml * (55 °C + 273.15 K)) / (36 °C + 273.15 K)
V2 = (295 ml * 328.15 K) / 309.15 K
Using the formula, we can calculate V2:
V2 = 313.28 ml
Therefore, the volume of the argon gas at 55 °C, assuming constant pressure, is 313.28 ml.
To solve this problem, you can use the combined gas law, which is a variation of the more commonly known ideal gas law. The combined gas law relates the initial and final states of a gas sample undergoing a change in temperature, pressure, and volume.
The formula for the combined gas law is as follows:
(P₁ * V₁) / (T₁) = (P₂ * V₂) / (T₂)
Where:
P₁ and P₂ are the initial and final pressures, respectively (assuming constant pressure in this case).
V₁ and V₂ are the initial and final volumes, respectively.
T₁ and T₂ are the initial and final temperatures, respectively.
Given that the pressure is constant (so the ratio of P₁ to P₂ is 1), we can simplify the formula to:
(V₁ / T₁) = (V₂ / T₂)
Now let's plug in the values from the problem into the formula:
V₁ = 295 mL
T₁ = 36 °C + 273.15 (convert to Kelvin) = 309.15 K
T₂ = 55 °C + 273.15 (convert to Kelvin) = 328.15 K
Now, we can rearrange the formula to solve for V₂:
V₂ = (V₁ / T₁) * T₂
Substituting the given values into the equation:
V₂ = (295 mL / 309.15 K) * 328.15 K
Calculating this expression will yield the volume (V₂) the gas will occupy at 55 °C assuming constant pressure.