Your muscles are switched on by releasing calcium ion from the sarcoplasmic reticulum that surrounds your muscle bundles. The Ca2+ binds to a muscle fiber, and that triggers the contraction. To relax the muscle again, Ca2+ must be pumped out, so that the concentration in the muscle returns to 10-6 M, and the concentration in th reticulum is 10-3 M. How much work is required per mole to move calcium ions
up this concentraBon gradient? (Hint: body temp is 37°C)
To calculate the work required to move calcium ions up the concentration gradient, we need to consider the change in concentration and use the formula:
Work = -RT ln(C2/C1)
Where:
- R is the ideal gas constant (8.314 J/(mol·K)).
- T is the temperature in Kelvin (37°C + 273.15 = 310.15 K).
- C2 is the final concentration (10^(-6) M).
- C1 is the initial concentration (10^(-3) M).
Let's plug in the values and calculate the work required per mole:
Work = - (8.314 J/(mol·K)) * (310.15 K) * ln(10^(-6) / 10^(-3))
First, let's simplify the equation inside the logarithm:
Work = - (8.314 J/(mol·K)) * (310.15 K) * ln(10^(-6 - (-3)))
Work = - (8.314 J/(mol·K)) * (310.15 K) * ln(10^(-3))
Since the logarithm of 10^(-3) equals -3, we can further simplify:
Work = - (8.314 J/(mol·K)) * (310.15 K) * (-3)
Work = 7704.34 J/mol
So, approximately 7704.34 Joules of work are required per mole to move calcium ions up this concentration gradient.